I resolved with no help from Wyze despite spending hours with their phone and chat support. The solution was on a reddit thread. Essentially, at least for this first batch of chime controllers, it is miswired internally so the instructions are incorrect. Just swap the colors as follows:
Wyze app instructions:
Chime Controller WHITE prong → connect to FRONT terminal
Chime Controller RED prong → connect to TRANS terminal
CORRECTED instructions:
Chime Controller WHITE prong → connect to TRANS terminal
Chime Controller RED prong → connect to FRONT terminal
Make sure the Chime setting is set to Mechanical in the app.