I'll use this table to figure out, once and for all, what happens in every extinction-related scenario, in every game.

Scenario Result
Action In other areas Pikmin Pikmin 2 Pikmin 3
Outside, lose your last Red. No Reds. No immediate action.
Next day, Red Onion spat a seed.
No immediate action.
Next day, Red Onion spat a seed.
Cutscene with the Onion spitting a Red seed.
Buried Reds. No immediate action.
Next day, in area without buried Reds, Red Onion spat a seed.
Next day, in an area with buried Reds, nothing happened.
No immediate action.
Next day, in area without buried Reds, Red Onion spat a seed.
Next day, in an area with buried Reds, nothing happened.
Cutscene with the Onion spitting a Red seed.
Outside, lose your last Pikmin. No Pikmin. Pikmin extinction cutscene. Sad liftoff.
Next day, all Onions spat a seed.
Pikmin extinction cutscene. Sad liftoff.
Next day, all Onions spat a seed. Ship didn't.
Impossible. If all five Pikmin are killed at once, there is a partial extinction process for each one.
Buried Pikmin. Pikmin extinction cutscene. Sad liftoff.
Next day, in area without buried Reds, all Onions spat a seed.
Next day, in an area with buried Reds, only the Yellow and Blue Onions spat seeds.
Pikmin extinction cutscene. Sad liftoff.
Next day, in area without buried Reds, all Onions spat a seed. Ship didn't.
Next day, in an area with buried Reds, only the Yellow and Blue Onions spat seeds. Ship didn't.
Impossible. If all five Pikmin are killed at once, there is a partial extinction process for each one.
Outside, turn your last Red into a Yellow. No Reds. No immediate action.
Next day, Red Onion spat a seed.
N/A Cutscene with the Onion spitting a Red seed.
Buried Reds. No immediate action.
Next day, in area without buried Reds, Red Onion spat a seed.
Next day, in area with buried Reds, nothing happened.
N/A Cutscene with the Onion spitting a Red seed.
Sunset, lose your last Red. No Reds. Liftoff with abandonment.
Next day, Red Onion spat a seed.
Liftoff with abandonment.
Next day, Red Onion spat a seed.
Liftoff with abandonment.
Next day, Onion spat a Red seed.
Buried Reds. Liftoff with abandonment.
Next day, in area without buried Reds, Red Onion spat a seed.
Next day, in area with buried Reds, nothing happened.
Liftoff with abandonment.
Next day, in area without buried Reds, Red Onion spat a seed.
Next day, in area with buried Reds, nothing happened.
Liftoff with abandonment.
Next day, in area without buried Reds, Onion spat a Red seed.
Next day, in area with buried Reds, nothing happened.
Sunset, lose your last Pikmin. No Pikmin. Liftoff with abandonment.
Next day, all Onions spat a seed.
Liftoff with abandonment.
Next day, all Onions spat a seed. Ship didn't.
Liftoff with abandonment.
Next day, Onion spat one seed of each.
Buried Pikmin. Liftoff with abandonment.
Next day, in area without buried Reds, all Onions spat a seed.
Next day, in an area with buried Reds, only the Yellow and Blue Onions spat seeds.
Liftoff with abandonment.
Next day, in area without buried Reds, all Onions spat a seed. Ship didn't.
Next day, in an area with buried Reds, only the Yellow and Blue Onions spat seeds. Ship didn't.
Liftoff with abandonment.
Next day, in area without buried Reds, Onion spat one seed of each.
Next day, in an area with buried Reds, Onion only spat seeds of the other colors.
Sunset, leave your last Red buried. N/A Next day, in area without buried Reds, Red Onion spat a seed.
Next day, in area with buried Reds, nothing happened.
Next day, in area without buried Reds, Red Onion spat a seed.
Next day, in area with buried Reds, nothing happened.
Next day, in area without buried Reds, Onion spat a Red seed.
Next day, in an area with buried Reds, nothing happened.
Sunset, leave your last Pikmin buried. N/A Next day, in area without buried Reds, all Onions spat a seed.
Next day, in an area with buried Reds, only the Yellow and Blue Onions spat seeds.
Next day, in area without buried Reds, all Onions spat a seed. Ship didn't.
Next day, in an area with buried Reds, only the Yellow and Blue Onions spat seeds. Ship didn't.
Next day, in area without buried Reds, Onion spat one seed of each.
Next day, in an area with buried Reds, Onion only spat seeds of the other colors.
In cave, lose only the Pikmin you brought. Indifferent N/A Extinction cutscene. Forced cave abandonment. N/A
In cave, lose your last Red. No Reds. N/A No immediate action.
After leaving cave, Red Onion spat a seed.
N/A
Buried Reds. N/A No immediate action.
After leaving cave, Red Onion spat a seed.
N/A
In cave, lose your last Pikmin. No Pikmin. N/A Extinction cutscene. Forced cave abandonment.
Outside, extinction cutscene. Sad liftoff.
Next day, all Onions spat a seed. Ship didn't.
N/A
Buried Pikmin. N/A Extinction cutscene. Forced cave abandonment.
Outside, extinction cutscene. Sad liftoff.
Next day, in area without buried Reds, all Onions spat a seed. Ship didn't.
Next day, in an area with buried Reds, only the Yellow and Blue Onions spat seeds. Ship didn't.
N/A
Outside, 99 Yellows + 1 Red in the area,
swap your last Red for a Yellow.
No Reds. No immediate action.
Next day, Red Onion spat a seed.
N/A A Red Pikmin is created inside the Onion.
Buried Reds. No immediate action.
Next day, in area without buried Reds, Red Onion spat a seed.
Next day, in area with buried Reds, nothing happened.
N/A A Red Pikmin is created inside the Onion.


Loose notes

What a mess this is...

Well, nothing happened then. The Onion will only eject a seed 1) the day after the extinction 2) if there are no Pikmin of that type planted somewhere on the area
2016-07-28 20:58:42	@Espyo	right
2016-07-28 20:58:45	@Espyo	that's good info to add
2016-07-28 20:59:30	Marty2000	For Pikmin 2, entering a cave and leaving it is considered as "a new day" (it's the same behaviour as P1, except that you can enter and leave the cave to have an Onion eject a seed, instead of ending the day)
2016-07-28 21:02:07	@Espyo	right
2016-07-28 21:20:41	Scruffy	So in /Pikmin/, there's an extinction cutscene only if you begin a day an area with no Pikmin of one type and there are no Pikmin buried there?
2016-07-28 21:24:38	Marty2000	Yes
2016-07-28 21:26:21	Scruffy	Cool, so that means it may not necessarily be an extinction if Pikmin are buried in a different area, but the game treats it as an extinction
<Marty2000> Espyo: "Outside, 99 Yellows + 1 Red in the area, swap your last Red for a Yellow." In P1, if you land in the same area, the red will appear in the Onion
<Marty2000> Same in P3 (tested yesterday)
...
<Marty2000> I have a single Yellow Pikmin awaiting its death and a White Pikmin ready to bring a corpse to the Red Onion
<Marty2000> by bringing a corpse to an Onion, the Onion will eject seeds
<Marty2000> it's only possible if the Onion ejects seeds
<Marty2000> A Mamuta/Snitchbug can't bury 100 Pikmin, only 99, but the Onion can make the 100th
<Marty2000> Ok, no Yellow Pikmin left, 100 Red Pikmin buried.
<Marty2000> The Yellow Onion ejected a seed!
<Marty2000> it didn't appear IN the Onion
<Marty2000> like in the other games...
<Marty2000> One of the buried Pikmin gets sent back to its Onion, I suppose

In this ^ case, P2 removes the buried Pikmin farthest from the Yellow Onion.

P1's extinction log entry triggers are simple: If in a given day, you got the cutscene with the on-screen "Pikmin extinction!" text, then that night's log will be about the total extinction. If at the start of a given day you got the cutscene where affected Onions spit out seeds, then that night's log will be about the partial extinction. You can also get the partial extinction entry on the day after a total extinction. Also, you only get these entries once per playthrough.

P3's extinction log entry only triggers if you let all Pikmin die via sunset.

Does the P3 Onion creating a Pikmin inside thing have a cutscene?