Mechanics and Fixing Any Questions Answered

Have a question about indexing - have never fettled MTB style shifters and derailleurs before, figured they work quite the same as road ones, but have just bought a secondhand tandem and can't seem to get the Deore M590 (I think) 9 speed rear shifter to work with the SLX derailleur. I have two issues:

1. Downshifting (i.e. into smaller gears) seems to be sticky - I have to downshift twice for the derailleur to move once (e.g. from 4 to 3 (it jumps to 2) or from 3-2 (it jumps to 1)), although upshifting (into larger gears) seems to be fine.
   
2. General indexing seems to be an issue even when upshifting
   
   

There doesn't seem to be a lot I can adjust - the only cable tension adjustment I can find is on the shifter itself; is this normal? I suspect it might be a cable and housing issue but I can definitely feel the shifter pulling on the cable as far as the rear bottom tube where the cable runs bare, and there are no visible signs of rust etc. (including on the RD, which looks pretty clean) because I understand the bike mostly lived indoors prior to coming into my possession. Would like to make sure I'm not missing anything before replacing the cables and housing (anyone know if tandems need special-length cables and housing..?)