Well the spring pulls the derailleur to the little cogs. The cable pulls it up the big ones.

Turning the RD barrel adjuster out (counter-clockwise) lengthens the housing, in effect pulling more cable. So if you have lazy shifting up the cassette, you need more pull. This is probably the case here, cuz you may have compressed the housing.

Find out by shifting to small cog. Shift up one at a time. If it doesn't shift, or is sluggish, give it a half turn out. See if it improves. Keep doing this until you can climb up the cassette with no issues.

Now go back down. There should be no hesitation. If there is, you need to turn the adjuster in. Go for quarter turns.

You may find that you can't find a spot where you can go both up and down without problems. If this is the case, you need to have a look at your cables, probably replace them. Very rarely, it's the shifter.

Also, I've been drinking. Apologies for any inaccuracies.