I believe the RCA connections may be meant to be connected to the amp's preamp outputs, not its speaker outputs. You might want to consult with the owner's manual, if you have access to one.
Many subwoofers deliberately favor one channel over the other. I mean, one channel will be arbitrarily suppressed (volume reduced) before the left and right signals are combined for playback. They do this because the low frequencies may be out of phase in the original left and right signals, and combining them directly would result in unwanted signal cancellation. Suppressing one of the channels would reduce this. The justification would be that low notes are fairly omnidirectional anyhow, so you would hear the same from either channel, and the suppression just makes sure there is no cancellation. Even with this, it shouldn't make a real difference if the channels are reversed.