The full wording is
"Score 8 VPs in a single round"
My guess is this is meant to imply, "Score 8 or more VPs during Phases 1 - 4 of one round"
Technically Cleanup is Phase 5 and still in the round. So one could argue that by claiming another objective first, it would allow claiming the 8 VP objective as well.
I realize this is most likely not the case, but if anyone has some insight either way it would be appreciated.
I believe the intent is the former, as you assume, to score during your turn before cleanup.