I noticed this most recently on ‘All of Me’ by John Legend - if you are playing the song full-speed, the app gives the one-bar count in, but if you slow down the tempo, it starts straight in on the first chord after you click (before you can even get your hands on your guitar). I have tried using the ‘back 10 seconds’ button to get all the way to the beginning, but it still omits the count-in - very annoying to have to play catch-up from the moment you start trying to play the song.
I have seen this happen with occasional other songs as well (will edit with titles if I come across them again) .
Edit: it also happens on “What’s Up?” at 90% tempo (but not at 100% or 80%, which is really weird).