1) Turn the bike up.
Note where the upper jockey wheel is lined up against the sprocket the chain is on.
Then turn the adjuster. This will take the jockey wheel away from the sprocket.
Now turn the adjuster the other way and it will bring back the JW into alignment.
All you need do is centre the JW on one sprocket and it should fall into direct line with each sprocket
2) However if the change from high to low is good then this would suggest that the cabling is sticking.
Changing from big sprocket to small sprocket relies on the spring in the rear mech and if the inner cable is sticking then it would cause the difficulties you are experiencing. You might need to clean the cables or put new cables on.
So try 1) and if that doesn't work look at 2)