Much like an encounter with a wild pet team, PVP Pet Battles are turn-based. However, unlike the PVE version, the PVP combat system is timed and any ability for each round must be chosen within that time limit otherwise it will assume you have passed a turn. A time penalty is applied if you take more than 15 seconds to choose an action, resulting in progressively shorter round timers for you.
Learned this today: posted a comment, came back later to see if there was any feedback, reloaded the page: the page posted a copy of my comment. That was not what I wanted. I just wanted to check if my comment was posted and if there were some responses. I did not want to post a copy of my comment from 5 hours ago. And, a humble guess, I think the majority of the users are not expecting such behavior either.