Yes, that is exactly the problem.

We do round 0 stuff.
We increment the round to 1 and process what happened.
We see WINWINWIN and set the round to 0 and do end of battle stuff.
THEN we do that check you cited.

I moved that call into the Round 0 section. I tested with a sausage golem and it worked fine.

Monsters in the QuestManager method that would have similarly not worked, had your autoattack killed the monster:

The demon version of your Nemesis (quest tracking) (as if you could kill it with auto-attack)
The Cake Lord (quest tracking)
GNG-R-3 (removing gingerservo)
X-32-F Combat Training Snowman (counting parts)
sausage goblin (preferences)
vote monsters (preferences and counters)

Revision 19463