The tooltips for Burning and Poison both say "start of each turn" instead of "start of each round". Players are confused enough about those terms that we don't need the game using them wrong too. Someone mentioned this on the Steam forums, and I confirmed it in keywords.csv.
That's why I had trouble when first starting, trying to figure out why certain things weren't happening at the beginnings of turns, and then getting confused between turns and rounds. Thank you for finding/fixing this, Kalin/BM. $8^ | (After all, by the time I understood how the stuff actually works, I wasn't studying basic tooltips like those anymore thus never noticed after I could've noticed. Ha!)