The pulley-cage tension spring has those obvious 2 or 3 settings, but the parallelogram tension spring, which is related to the problem here, is not adjustable.
However, the pivots are adjustable, and I suspect 1 or more of them are adjusted too tight--and if loosened a little, will permit the spring to pull the chain onto the smaller sprockets just fine. The 9mm-head bolts are threaded into the parallelogram arms, then into the locknuts behind them. The play is adjusted just like the double-nuts on the centerbolt of a sidepull brake. It might be easiest to take the derailleur off the bike to adjust it. Unless the spring has been bent or abused somehow, it should have enough strength to work OK, if the links pivot freely as they should, and the cable (both inner & outer) is good. A little well-placed oil always helps too.
In your first pic, it looks like the cable is clamped incorrectly. In the 2nd photo, I can't tell; maybe it's been corrected there. It should go right thru the little hole in the top of the special folded-over washer. If it's not clamped correctly, that will also degrade the shifting.