Are you sure the doorbell chime requires 24VAC? Most doorbells we install only require 16VAC. I am sure the 24VAC wouldn't hurt the chime, it just needs enough voltage to power the coil but I would check this as a 24VAC transformer may be outputting up to 30VAC. I have installed multiple 16VAC transformers that output at 19+VAC.
Are you certain you have the door bell chime wired correctly? If you connect both the Chime and Nutone station together and neither work, this may be a wiring problem and not a compatibility issue.