according to my alldata, the oil pans have different part numbers:
I looked them up as 1990 crx si and 93 civic si
the 90 comes back as 11200pm3020
the 93 comes back as 11200p08020
I don't know what the difference could be, but they def have different part numbers.
unless your pickup tube isn't in the oil it should be pumping the oil to the engine.
Remember that the oil pump is a positive displacement unit, it can only move what is there, also remember that the inside of an engine is just one big controlled oil leak, if your bearings are the wrong size or you have a crack in one of your main oil galleys then you won't be able to produce oil pressure.