The calculation is based on the advancement in the music, it can literally not be off beat. There's a built in function in game maker that check for the position in a song. I put the beat on every half of a second of advancement in the song (120 BPM) (not actual time, pure advancement of the song as it is played, lag included). So technically speaking, it resets the "check" as you say, every single second. If there is lag and the song slows or speed up for some reasons, it would not change anything and the beat would still line perfectly for the simple reason it's locked to the song itself.
Also I composed every single song apart from the one in level 5.
And they are all 120 BPM since I never touched on the parameter in PTCollab so that it would make things easier for myself.
Once again, that might be a problem with your machine or something. A problem THIS big wouldn't have gone past under my nose, especially since I had a team of 7 play testers who played the game in full on various platforms.