Are they physical chimes, or does it play an electronic sound?

If physical, maybe the solenoid is sticky and doesn't finish its chime cycle for a few seconds.

Or maybe the button itself is sticky, and so when you take your finger off the button, it's a few seconds before the solenoid releases and the second half of the chime sounds (and the first half of the chime is malfunctioning and silent, and the dogs are responding to the buzz of the solenoid, as I mentioned in my previous post). Our doorbell had the sticky button problem for a while until I fixed it, and the solenoid would stay stuck "on" for random amounts of time.

Oo, here's an idea. In my childhood home there were several chimes, the thing would play a full melody on a set of tuned physical tubes. Maybe the first few notes are malfunctioning on your melodic chimes, and only the final note rings out for you, and again, like in my earlier post, the dogs are responding to the buzz of the solenoids activating.