I don't know how normal that is. It sounds to me like your rest is too far to the right (an arrow width inside the string).

I've never cared about paper tuning, never even tried it. I'm an archery hunter, not an archer that also hunts. All I care about is good arrow flight. If the broadheads and FPs are both flying right, and to the same POI throughout my hunting range (out to 30 yds), that's what I want. A dead deer won't critique your paper tear.

BUT, something about your rest being that far in makes me wonder if you are shooting the right arrow, if you have fletch contact, or have some form issue.