Just got a new Marin four Corners. It has a 50/36/30 in front and 9 speed 11/32 in rear.
I'm having issues on the rear. I shift down (to a larger cog) and oftentimes it drops up a gear (to a smaller cog) This has happened consistently and usually on the larger 4 rear cogs. I will shift to a larger and it will drop back to a smaller. Here's the weird thing. Sometimes after I physically shift, it will on it's on shift back and forth. In other words, I'm pedaling along and it drops to a lower gear, then back up then back down.
It is as if the derailleur is indexing BETWEEN the rear cogs and it can't quite decide which one it is supposed to be on.

So I shifted to the smallest cog, loosened the cable lock nut and pulled the slack out of the cable. Still does it.

So I'm thinking I need to make an adjustment on the rear barrel adjustment. (?)

Do I adjust the barrel to tighten the cable tension or loosen, and does it tighten by turning counterclockwise or clockwise?

I should mention the limit screws seem to be dead on.