Look at the adjuster and the cable housing when you turn it. If the cable housing get's pushed out from the barrel adjuster, it is "tightening the cable" because it is in effect lengthening the the overall length ofcable housing. If the cable housing get's pulled into the barrel adjuster, it is "loosening" the cable because it is in effect shortening the overall length of the cable housing.

Tightening the cable (lengthening the cable housing, whether that be by using the inline or the adjuster at the derailleur), moves the rear derailleur inward, towards the larger sprockets. You can see this happen more readily by messing with the derailleur-mounted barrel adjuster. Turn it so it moves outward from the derailleur (counterclockwise turns): this "lengthens" the housing, tightens the cable and moves the derailleur inward.

Loosening the cable (shortening the cable housing, whether that be by using the inline or the adjuster at the derailleur), allows the rear derailleur to move outward by spring action, towards the smaller sprockets. You can see this happen more readily by messing with the derailleur-mounted barrel adjuster. Turn it so it moves into the derailleur (clockwise turns): this "shortens" the overall housing length, loosens the cable and allows the derailleur to spring outward.

Here's how to really tune in your index shifting, assuming it has full range small to large, but just isn't shifting crisply. It really only takes a minute.

Shift into one of the middle cogs. Doesn't matter which one. Doesn't matter if it's a little noisy at this time.

While pedaling the bike, turn the cable adjuster counterclockwise slowly to cause the derailleur to shift on it's own to one cog larger. In other words, you're not doing anything with the shifter, just tightening the cable. Stop adjusting as soon as it shifts.

Then, moving the barrel adjuster 1/4 turn at a time the other way - clockwise - turn the adjuster clockwise until it shifts down to the "correct" cog, and keep turning it clockwise until it just shifts onto one cog smaller. Again, stop right when it shifts. Count the 1/4 turns while you are doing this. From the "larger" to the "smaller" cogs it will probably come to something like 15-18 1/4 turns, but that number doesn't really matter as long as you count. It's easy to count, because that barrel adjuster at the rear derailleur has detents every 1/4 turn.

Then, turn the adjuster back the other way - counter clockwise - counting your 1/4 turns and stop at 1/2 the number you counted when you went from "one cog too big" to "one cog too small". This will cause the derailleur to move back to the "correct" cog, but it will be exactly in the middle of the correct cog, not a little one side or the other. This should give you perfect shifting.