My simple answer.. A oilpump just needs to be driven by the engine.. there is no "timing" involved. The pressure the pump makes is going up with the engines rpm's.. that's normal, if you have a warn engine the oilpressure can get to low.. a good check for that is looking at the oil coming on the casmshaft when you turn the engine rpm's as low as 500 rpm, the cam should stay lubricated at that enginespeed, check it through your oilcap opening when the engine is idling.
Your car is probably idling at a higher rpm as it is a automatic..
About that auto.. if you change to a 5 speed change the diff as well.. as a auto has a 3,5 diff of even 3,3? A 5 speed needs a 3,7 or3,9 otherwise you use a lot of clutchplates as the 1st gear becomes very long.