I can't speak of what Genos, Tyros, or PSR-S models do, but what I've noticed on the PSR-E models I've used is that if I set the Tempo on the keyboard, record a User Song, convert the User Song to a Standard MIDI File, and then look at the data in the SMF, the Tempo is slightly off from an exact value.
For instance, if I set the Tempo to 96 BPM, the MIDI file will end up with a Tempo that's something like 95.xxx or 96.xxx BPM-- very close to 96 BPM, but not exact.
The odd thing is, the format of the Tempo within the SMF should allow for either an exact value, or-- if an exact value isn't possible for the specified Tempo-- for a value that's closer to the specified Tempo.
I'd have to make some test files to verify, but it's as though the method Yamaha uses either to store the desired Tempo, or to compute the equivalent MIDI value from the desired Tempo, isn't using as many significant digits as it should be, such that it's coming out as a value that's nearly correct, but ever so slightly off.