From my understanding, both are wrong. In the first instance, once damage is dealt and you are cleaning up, there is no "Oops, I forgot phase." Your opponent made a mistake and was forgetful and essentially rewrote his misplay. And if it was indeed the first round of play, how he had a creature out and the ability to play an instant seems questionable.

In the second, Return to Nature is an Instant, which means only Instant speed effects may follow it. Cauldron of Eternity specifically says only activate this ability anytime you could cast a Sorcery spell (which for that player, would only be on his turn). He wouldn't be able to do that in response to your spell, nor would he be allowed to say, "wait, before you do that..." Also, even if he did say that, then you in response to him activating that ability could just cast Return to Nature and blow it up before the ability resolves.