Hello and welcome to OF.
First of all, nice watch! I think it’s 168.0
29?
Looks like nice example. I was going to first ask who stays up to watch the day/date change, but I recall I was staring at my first vintage Omega well into the wee hours…..
I have a serviced cal 751 Constellation from 1967 and the day and date snap over almost instantly at midnight, so that’s what is supposed to happen. However I have other vintage watches that change a bit early or late, like yours. It is likely a minor fix at service, but I wouldn’t worry in meantime just have it checked at next service. I’m sure watchmakers here can explain what needs to be done
So welcome and stick around, you will likely add to your collection! Good hunting.