The Tap Tempo is simply not implemented yet. How it could work is to provide a parameter that could be mapped (like “Manual Retrigger” in LFOs) that would react to taps and adjust the tempo.
Btw, is the ‘down beat’ the first beat of a bar?
Using SysEx to signal this is not standard, normally it’s done by sending a Start message or Song Position Pointer, then producing the Clock messages at the required rate. I’d be interested to know which devices make use of the Axe Fx’s SysEx message. 