2 New Doorbell Pros - Single existing mechanical chime

I recently installed 2 new Video Doorbell Pro units in a new construction home that came with a standard mechanical chime, and 2 standard doorbells. Although the doorbells are working and recording video, I apparently am missing something as the mechanical chime is not working. I installed the 2 Power Pro units that came with the 2 doorbells, but no combination of wiring seems to work. I also purchased a hardwired transformer from Ring, currently not installed, and unsure if it's needed. Can someone point me to a wiring diagram for this scenario and clarify whether the hardwired transformer is necessary in this case (2 Video Pros, 1 existing mechanical chime)? Thanks!