Heuer Monaco (re-ed) loose pusher - needs periodic service
It is generally recommended that a mechanical watch be serviced (disassemble, clean, oil, adjust) every 3 - 5 years. This will solve the inaccuracy issue and the watchmaker will properly re-attach the pusher. Yours is way overdue for such a service. The pusher is probably held in place with a set screw which has come loose. That is often the issue with crowns that fall out of the movement. You can either send to Tag Heuer, simply take to a Tag Heuer authorized dealer or utilize a local, trusted, watchmaker.