Ok, to check if the power supply has a rectifier built in all you have to do is. . . with the unit unplugged, check for continuity on the secondary winding of the transformer, now swap the test probes of your DMM round and see if you still get continuity.
If you only get a circuit one way, and open circuit the other, then your power supply is rectified. (and likely not filtered, which would explain why it's confusing your multimeter)
If you get continuity both ways, then your power supply is either a)NOT rectified or b)the rectifier is shorted