If you kill the cave troll with the finger of death spell, do you still have to roll to see if the troll regenerates?

I would lean on yes. Cave Troll says to roll when you defeat it. Finger of Death says it is killed. Rules for battle say "If the character’s attack score is
higher, the creature is killed." (p. 10).

Is defeat tied down to just combat result you get after rolling dice or does it apply to all things that will kill the Cave Troll is the question.