I just fired up HPTM on both devices to check and they're both running 1.3.7. Whilst there, I started the tournament running again and connected to it, then used the timer slider to get the level to the last few seconds, and wouldn't you know it - everything behaved the way it should this time. Even tried locking the phone, and putting the app into the background during a level change, and it was all fine. If it happens again, I'll try to note anything special about the circumstances.
Doing that did remind me of another (very minor) issue - the upper left and right corners of the main tournament screen are being rendered outside of the view port, truncating the start of the title, and the end of the "Time to Break" and its timer when running.
Here's a screenshot from my Surface Pro 6, which is acting as the tournament server: 
