To confirm the MIDI routing, is it FCB-1010 –> AdrenaLinn III –> TimeFactor?
The ADR III System Sync (bottom row – second knob) should be Out or i-o. The TF should have CLK In = On, and OUTPUT = THRU. The AdrenaLinn will be the tempo master.
If the MIDI routing were FCB-1010 –> TimeFactor –> AdrenaLinn III, I can see where program changes and CC messages would pass [OUTPUT = THRU], but tap tempo wouldn't work. That would require CLK Out = On, and OUTPUT = XMT for the Timefactor to be the tempo master. The ADR III would follow the TF clock with a Sync setting of in or i-o. Unfortunately, OUTPUT = XMT would then block all MIDI messages coming from the FCB-1010.
I have a similar routing for part of my MIDI chain.
–> External Clock source / tap tempo -> FCB-1010 (MIDI Merge On) –> PitchFactor (OUTPUT=THRU) –> ADR III (i-o) –>
That helps to get around the Factor pedal's "either-or" MIDI Implementation. Either you transmit MIDI, or you can receive MIDI and pass it on through. I'm not sure if any of this will help you out of your situation.
There are a few different routings to explore, and some of them involve compromises. For example, you can use an FCB-1010 switch to tap tempo to the TimeFactor and/or AdrenaLinn. And a few more settings in both devices that could be stopping you cold (PSt or dbt as a Tempo Source, rather than SYS in the AdrenaLinn, for example). A few more details would help here.
BTW, my audio routing goes in the opposite direction. The Adrenalinn III is the border between my mono signal / effects and the stereo ones that follow.