question about the mission "frenzied dance"

after i read over the text, i just wonder what is the timing when u make sure "conquer the ziggurat"? do i resolve in my active turn when i control a active character, and when he achieve the goal it immediately counts as i conquered that ziggurat? or anytime a character make the goal?
for example, now we have two character in one ziggurat, one from me and one from my opponent. it's my active turn, i shoot the enemy character down in that ziggurat with another character outside that ziggurat, do i immediately count as conquered it?
another example, even if you clean up all the conquer token at the end of the round, if my character still stand in one ziggurat alone, do i automatically conquer that at the start of next round?

and beside those above, do i still conquer the ziggurat when i make my character leave the ziggurat after i conquer it? if i move a character inside a ziggurat, conquer it, and then move out, what will happen?

 

wow didn't notice that, thanks a lot~