You're essentially connecting to a peer to peer service, just like downloading a torrent. Your IP is viewable to anyone and everyone inside that connected swarm. I'd highly advise getting a VPN with IPV6 leak protection, otherwise you might indeed find yourself getting a call from your ISP or a letter saying you've been caught doing something against copyright. The first couple of times, you'll just get a letter, but eventually, they might cancel your service and you won't be able to get another since you're blacklisted.
Worst cases, people have even been taken to court, and popcorn time is a big target for DMCA requests.