Apparently the byo-yomi sounds work in such a way that they can be skipped if you have a laggy connection.
See also this topic where I had the same experience: Byo-Yomi countdown suddenly gone
Personally I think that it would be better to have the client start beeping without confirmation from the server, especially since byo-yomi is such a time-critical part of the game. The other users in my thread did not seem to consider it a problem.
Maybe there are some advantages to the current implementation that I am not aware of, or it’s just not a high-priority change for the devs.