I'd almost be willing to bet
that your press is not installed perfectly level--that it pitches forward, towards you. Add to that the fact that you are learning how to stroke, and the result is that when you index the press, the case can 'slip' slightly, throwing it out of alignment with the die above.
Verify that your bench is level--and that it is stiff enough so that flexing will not also cause case movement in the shell holder as you stroke.
For now, try this: Rotate the shell holder, so that you have to insert the case 'at an angle'--and see if that helps. If it does, that suggests that the case is moving in the shellholder during the indexing stroke. If it does not, it suggests that dirt in the shell holder rim is canting the case when you insert it into the shellholder. Clean the shellholder, inside the slot that holds the case.
I can have this same misalignment problem on my (standard) turret--and it is because my benchtop is not perfectly level (and for reasons not covered here, I cannot readily change it to perfectly level). For me, the problem is only with the taller / smaller-diameter cases, like 357 Magnum and 10mm, and it can occur when I have trying to work at higher production levels (say 200+ rounds per hour).
What I have done is learn to do a slight 'movement' that is now a habit, and fully integrated into my 'muscle memory' for reloading. I simply push against the case with my (left) thumb as I start the stroke to guide the case into the die mouth. This does take some dexterity and practice, BTW--you don't need to pinch that thumb between the ram and the die--or worse, get it in far enough to cut it on the rim and die. But, once you slowly get the feel for it, it can become habitual, and there is no significant hazard
Also, be sure to review the indexing adjustment when you put the rod back in. IMO, using auto-indexing when loading handgun cartridges (i.e., most straightwall) is the best way to work--but setting up the indexing and learning the stroke for smooth operation does take some practice.
Jim H.