The only solution I have found is clicking (in the move list) each individual move, it's still a hasslr but not nearly as bad as having to scroll all the time.
The computer analysis thing

I agree -- this is a real hassle and it would be great to see it fixed. The screen basically refreshes after each move. As zxb995511 mentioned, the only workaround seems to be to click the moves list itself and not use the arrows at all.

Was this fixed since posted? I don't have this problem, the arrow clicking always highlight the current move without popping back to initial moves.

Skepticus. We are talking about the moves in the box...the highlighted moves of "1.d4 Nxe5", not the movements of the pieces.

It depends on your monitor resolution as well, if you minimize all your toolbars in the view part of your browser then it will not jump because you don't need to scroll to see everything.

@Afa, I'm talking about that too. That box, in my case, don't go back with every click on any arrow. I can follow all lines: played ones, recommended and alternative without the popping back problem, just clicking on the arrows. It would annoying to me too if I experienced the problem you describe. But if I don't, maybe the settings, software and/or hardware configuration that I use can help. To you or to the support to figure out what's happening.
@Loki, in my case I can't see all the box at the first time, I just scroll a bit down to see it with the board but it doesn't pop back at described by who has the problem. It must be another thing.

When I try to use the arrow keys to go to my next move in the computer analysis, the box with the moves in it just pops back up to showing the first moves...it doesn't follow along with my buttons so I have to scroll down each time to see which move is highlighted...and then it pops back up again when I click on the forward button again. Frustrating.