The "correct" way to send tempo is via midi clock. This is because it is not only giving you the right tempo but also a SYNCHRONIZED tempo, i.e. all the beats starts at the exact same time.
I don't know if the Superswitcher could send midi clock, but if it is the case I strongly suggest that you explore that route. I also found out that the M5 will also respond to midi clock.
If the SS2 doesn't generate midi clock, since you said that the M5 is responding fine with your current setup another option would be to see if the M5 transmit a midi clock based on the tap tempo received. If this is the case you could then use this midi clock, provided that the H9 is after the M5 in the midi chain.