That seems like it's the exact opposite of what it's supposed to do.
If I put the fob in the fobgina while I'm driving, I get the chirp only if I turn the car off
and open the door without removing the fob. The only time it chirps like that is if I leave the car running and step more than a few feet away from the car with the fob in my pocket.
Hopefully, the dealership isn't too far. I would go back and make them prove to you that another Z on their lot does it, too. I'm assuming the recent service was not related to this issue.