My family was there a week ago, on June 9 & June 10.
We were on Tom Sawyer Island from about Noon - 1:15 on Saturday 6/9. We walked through the performance area when we first got off the raft; then about half an hour later the kids asked to see if there was a show over there. So we walked back to that end of the island. We got there about 12:45 and the show had just ended and the CMs were re-setting all the props for the next show which wasn't until 2:30. We have APs, so we all agreed to try and see it next time.
The Entertainment Times Guide that they give you when you walk into the park only had the hours for the rafts. The show description just stated: "And don't miss a real, live swashbuckling adventure, in which Jack Sparrow crosses swords with a back-stabbing crew of scoundrels!"
So if I have to guess, the shows are 2 hours apart, starting at 12:30. Maybe the Entertainment Guide has been updated and someone can post if there are show times listed?