Hi Hans,
first of all, OTS cannot change split points, Registrations can.
The reason for the described problem (R1 and R2 voices cannot be heard when R3 is additionally switched on) is always that the R3 split point is set slightly higher than the correct setting (which is, as mentioned, exactly one semitone above the Left split point.
I recommend to leave the Split Point settings display open while switching between the Registrations and OTS with which the problems occur. You probably will see that the split point settings are changed by your Registrations. In this case I would lock the split points (as mentioned) in the "Parameter Lock" display. (You can still manually adjust the split points directly in the split point settings display if needed.)
P.S.
As already mentioned, OTS cannot change the split points. But OTS can of course switch the ON/OFF status of the keyboard parts (just like Registrations).
For example, suppose the Style and Left split points are both set to F#2. If the R3 split point is accidentally set to G#2 instead of correctly set to G2, the R1 and R2 voices would only be heard on a single key (namely G2) when R3 is also switched on. It does not matter whether R3 is switched on manually or by an OTS or by a Registration.
Hope this helps!
Best regards,
Chris