Can Postgres timestamp be used to implement client side caching?
I assume that your problem is that when you see a row with a certain timestamp in the table, you want to to be certain that a later query cannot find a new row with a smaller timestamp.
There is no good way to guarantee that unless you serialize processing, which would be bad for performance.
You might use a workaround: if you know that none of your transactions can take longer than 0.1 seconds, consider rows with a timestamp later than current_timestamp - INTERVAL '1 second' as not yet reliable.  This is a heuristic that can go wrong (I/O overload might make your transactions slower than you think), but it should work out most of the time.