to fall suddenly and helplessly
to turn end over end in falling or flight
to roll over and over, to and fro, or end over end
So tumble can mean roll, or a rolling fall, but it can also just mean a general fall.
in the direction of and into contact with
in contact with
So against can mean something is already in contact with something else (the chair is up against the wall) or that something comes to be in contact with something, as in your example sentence:
She tumbled back against the slick, damp wall.
Here, she fell helplessly (rather than rolled over) and came to be against the wall.
It can't mean "she rolled back on a sloping wall", because "against" doesn't indicate a continued movement. We would need words such as the following instead:
she tumbled down the wall (assuming it is sloping!)
she tumbled across / around / along the floor
Note that in these sentences, tumble would probably indicate a rolling action because of the continuity of the action - even falling down the stairs would be a tumble!
As "against" doesn't indicate this kind of continued movement, "to tumble back against" is a one-off fall, not a rolling action, that meant she hit the wall - and "back" just tells us that she fell backwards, not forwards.