Zhar question

By Zapranoth, in Arkham Horror Second Edition

So this'll seem a dumb question, but just to be sure:
In final battle against Zhar, does it work like this?

Round 1: investigators upkeep, then attack, then Zhar attacks and first investigator gets the Zhar token.

Round 2: upkeep, then investigators attack -- but first investigator is same person as it was last round, and he/she gets only one hand. When Zhar attacks, this first investigator is then devoured.

Round 3: upkeep, remaining investigators attack; new first investigator gets Zhar token as Zhar's attack.

Round 4: upkeep, first investigator gets only one hand; Zhar attacks, current first investigator devoured...

etc

... ?

Sounds right to me.