I can share my own (positive) test, which confirms timestamp and id theory. My test was taken on the 7th January, it was a rapid test, not a PCR. But it's in the same government database:
https://pcr.euprava.gov.rs/validate.php?cqcode=1641591150Q!A...
Timestamp: 1641591150, which translates to GMT: Friday, 7. January 2022. 21:32:30. That seems to be right, it was taken earlier on the 7th and probably entered later to the central database.
Also, ID of my test is: 7601263. Djokovic IDs are 7371999 (16/12 test) and 7320919 (22/12 test).
It really looks like IDs are incremental, and that his test that was supposedly taken on the 16th was taken on the later date.
One consolation fact is that he wasn't positive when he took photos with kids on 17th.
EDIT: I messed up and copied Novak's QR url! fixed now!