The BPM will likely fluctuate on the display while the A4 works out a tempo based on the clock.
When tempo is calculated from a MIDI clock, it’s actually not a lot different from you using the Tap Tempo functionality. It will likely take a couple of seconds before the device averages out the intervals in the ‘taps’ and shows a more even tempo.
Tempo is not just sent as a numeric value, it’s calculated over time from the MIDI clock pulses, so it relies in this case, on your DAW/MIDI interface having good timing!
Sorry if that was obvious, just clarifying 