Installing Tub Surround

a gap, I am installing a tub surround on top of the backer board,,,

Check the installation instructions for surround ... in general, you must install the board lessor flush the inside edge of the lip around the tub so that can slide up above the lip. In other words, to end the support board above the tub where it will meet so you can position the bath to be under the board for the atmosphere to come down to align with the inner edge of the tub lip. You may have to shim the tub lip to attach to poles.

Do not put anything on the walls surrounding the tub is attached directly to the studs with glue and nails or screws and just on the bathtub.