Does Skill Swap reset on the user too if switched out?

Question

I was playing doubles on Pokemon Showdown, I had a Regenerator Reuniclus with Skill Swap, and one of my opponent's Pokemon had Moxie. I thought that the ability swapping reset if switched out. Ie, Reuniclus uses Skill Swap to make the opponent's ability Regenerator, which is useless because it'll reset when they go back into their Pokeball and they won't heal anything. Likewise, Reuniclus, though swapped its Regenerator away, would regain Regenerator upon switching out and recover its HP.

So I Skill Swapped Moxie away from the opponent, and being that he was down to his last two Pokemon, he couldn't switch it out, so it was stuck with the useless Regenerator. I swapped out Reuniclus since it had 1/3 of its health and I was like "well she did her job here." Later when I sent her back out, she still had Moxie apparently and didn't recover health despite switching. Bulbapedia says, "If a Pokémon affected by Skill Swap is switched out, it regains its original Ability." Reuniclus was affected by Skill Swap, therefore she should have regained her original ability. Unless it means, only the Pokemon it's used on and not the user...?

Comments

By any chance, can you show us a replay? If not, can you try to reproduce the "ability not resetting" and show us a replay of that?

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https://replay.pokemonshowdown.com/gen7doublesubers-682416020 recreated, but also with the other person swapping out. Regenerator stayed on his Pokemon even after swapping out, and it recovered their health, while Reuniclus swapping out still had Moxie and didn't get her health back.

Answer 1

Regenerator restores ⅓ of the Pokémon's maximum HP upon switching out.
This effect will occur if Regenerator is the Pokémon's Ability in battle when it switches out and is not suppressed; a Pokémon that obtained the Ability with Trace will restore HP when it switches out, whereas a Pokémon which has Regenerator but has been affected by Gastro Acid will not.

source
In other words, regenerator restored Krookodile's HP before it reverted to moxie. Unfortunately, that means Krookodile had to wait until after it switches out in order to continue drinking its soda.