Can you win syndrome during someone else’s turn?

If you have already defeated the omnidroid Vx.10 the only other thing you have to do is clear your realm of heroes... if you use the condition bio probe (if someone defeats a hero defeat a hero of equal or lesser strength) to defeat the last hero... do you win? Because syndrome doesn't have a start your turn objective... it just says 'defeat pani droid Vx.10 and have no heroes in your realm'