I quoted you both because you two have the same concern, don't worry about the timestamp at all, NO, you won't lose a block because your clock is half a minute late/early, you can even mine blocks with a timestamp in that past.

If block 100 is mined at 2:00 AM and you manage to solve block 101 with a timestamp of 1:50 AM, it will still be accepted, there are basically two rules for the timestamp of a block, it can't be more than 2 hours into the future based on your node network adjusted time, and it can't be lower than the median time of the last 11 blocks.

As for the online explorers, some might be showing the timestamp on which they received the block based on their own clock, some will show the timestamp that is in the block itself, clocks are never 100% synced so all this variation is completely normal.