Most RD's I've seen default to the smallest cog when there is no tension (or lowest tension) on the RD shifter cable. Increase tension on the cable (and stretch the RD spring) by pressing the largest lever on trigger-shifters, or moving the brake lever on brifters, usually down-shifts to the larger cogs. Releasing the tension up-shifts to smaller cogs.
This seems backwards to me. It's not backwards from how the FD works, but it's backwards in terms of upshifting (lower cadence, faster speed), or downshifting (higher cadence, lower speed). Indeed after riding for months I still get my rear shifting backwards by hitting one lever when I meant to hit the other from time to time.
But it seems like I saw a video once showing how to adjust an RD that had its default position under the largest cog on the cassette, and increasing cable tension moved the chain to smaller cogs. This would make both levers on both shifters operate the same - large lever (or brake lever) for up shifting, small lever for down shifting. Is there a name or term for each type of RD, one that normally sits closer to the wheel, and one that sits farther away? Have searched Sheldon's site but didn't see anything relating to RD positioning.