The Roku live stream is approximately 30 minutes behind iOS. I tested my Tv app comparing iOS, Android, and web. I used both HLS URLs (w/ and w/o tags). Removing the tag had a minimal effect, perhaps a few seconds difference, but the discrepancy between platforms is much greater. After loading the same streams in both environments, we are seeing a delay of *many minutes* on different devices.
This can happen if the live stream isn't sending you just the live segments but also previous ones. On some players you can tell them to play it live, no idea if Roku has such an option. I'm curious to find out as well.