Maybe the chimes actually do ring immediately, but the electronic emitter doesn't play it loudly enough at the beginning. For example, maybe it repeats the melody three times instead of twice and you're not hearing the first one because it's not sending enough DC voltage to the emitter circuit at first. Maybe the voltage ramps up. And the dogs are hearing the quiet bit, but you're not.

Or maybe it's something to do with that talkback microphone you described. Maybe the button press engages the talkback mic, which (by design) delays/mutes the chimes, and the dogs are responding to the noise of the faint sound coming through the talkback speaker, or even just the faint click of the talkback system engaging at all.