Considering that oil pressure is measured "upstream" from the filter element, it doesn't seem likely that a clogged filter could be the culprit. A poor filter seal, however, could be allowing the filter housing to empty while the engine is not running, resulting in a delayed oil pressure indication.

In summer weather conditions, a delay in oil pressure cannot reasonably be the fault of the oil. You could fill the oil sump with water and get good pressure a lot faster than 12 seconds, assuming no other factors were involved.