Sure this is right?
I inspected player above me, and his current active team was not the same as I was fighting in Space Time.
About fighting against 9tail teams, it would make sense that players get into their 9tails team and end up doing a Space time battle with the wrong active team while waiting for the world boss event to start.

The way I thought this was working is that once you do a fight, your team lineup gets stored - the same way as Ranked battle works, where you actually need to fight something to update your power.