Still don't really understand your terms, but I'll try.
By "opening at the saved tempo," do you mean that when you hit the right switch it shows the saved tempo on the display ?
By "non-synced preset," do you mean saved with Tempo off ?
Can I assume that Global Tempo is OFF ?
Assuming the above are true, the behavior is what I would expect – if Global Tempo is off, the tempo will be loaded from the preset with a default value of 120BPM. You can always change the tempo and save the preset – then it will reload with the new value.
