Sounds as if you have a 7-speed shifter, too. The RSX rear derailler doesn't have "speeds" and is compatible with Shimano 6, 7, 8, 9 or 10-speed systems, as long as the number of speeds in your shifter match the number of sprockets (and in the case of 6-speed freewheels, there were a couple of different spacing variants back in the day).
The main culprit in your having to adjust the rear derailler each time you switch wheels is the spacing between the cassette and your bike's rear dropout. One of the cassettes sits further away from the dropout than the other.
So, you should
1) find the wheel where the cassette sits further away from the dropout (which is unnecessary and only increases the dish of the wheel, making it weaker)
2) remove a spacer from the drive-side axle and stick it over on the non-drive-side - if the difference is only 1mm and you have only a 2mm spacer on the drive-side, you may need to buy two 1mm spacers
3) re-dish the wheel since the rim will now be slightly too far toward the drive-side