Hey Cosmin, thanks for sparing some time for me

.
Before speaking of anything musical, I need to get rid of something about guitar technique which is bugging me for way too long.
For that cause, lets consider this basic major scale shape:
---5--7--9------------------------------------ (I don't know how to post tabs with forum tools so I typed by hand)
------------5--7--9-----------------------------
---------------------6--7--9----------------------
------------------------------6--7--9----------------
---------------------------------------7--9--10--------
-------------------------------------------------7--9--10
Back then, I was playing scales, or lets say basically anything related with alternate picking with only one of my finger touching to frets. For example, to play 5--7--9, I put my index to 5 and pick the string, after that I lift my index finger and put my middle finger to 7, and so on..
This type of play is maybe fine for going down, but when it comes to playing backwards (like 9-7-5) it sounds so bad I can't even find the words to describe how terrible I feel. It sounds very unconnected, there are little gaps between notes which you can't hear exactly but enough to take away all the musicality, the flow of music.
I asked my former guitar instructor about that. He said, to play these type of partitions, I should do a kind of "spider-walk" on the frets. For example when a triplet like 9--7--5 appears, I must put my pinky finger to 9 and middle finger to 7 simultaneously. For a while I played like this but the problem was still there.
Now, I'm trying to incorporate pull-offs to play these, e.g. to play 9-7-5, every finger takes their place at the same time and, for example when going from 9 to 7, I both pick the string and pull off to the note. Playing like this sounds better than anything else I came up with, but still, STILL it didn't disappear completely.
I seriously need to get rid of this for whatever I play it simply does not sounds right. I'll post a rec as soon as possible for clarification. And again, thanks for taking me on