Thanks @Leiya_Kenney for the quick response!
To clarify, the timestamp field I am talking about is the one appearing on etherscan.io (not sure if there are more). When looking at blocks on etherscan.io, the timestamp’s info box actually clearly says that this is the date and time at which the block was mined. This is confirmed when looking at next and previous blocks, e.g.
timestamp: 10:03:42 PM +UTC
mined by: 0x1000 in 12 sec
timestamp: 10:03:50 PM +UTC
mined by: 0x1001 in 8 sec
timestamp: 10:04:20 PM +UTC
mined by: 0x1002 in 30 sec
All transactions in block 1002 will have that same timestamp, 10:04:20 PM +UTC.
My issue is that I will receive the logs of a transaction included in block 1002 not before 10:04:23 PM +UTC, that is to say at least 3 seconds after the block is mined.