How to fix dry wall side of newly fitted tiles shower wall?
If you're seeing that water on the drywall on the other side of the wall opposite where the tile is then your shower was not installed with a proper membrane. You need a waterproof memberane and a suitable substrate for the shower.

This would be something like kerdi and/or a tile backerboard painted with redgard. You cannot use drywall to back it, nor can you use "green board" in most states. You need a cement board and/or a waterproof membrane.

Demolish and replace the shower ASAP. The more you allow water to penetrate that wall the bigger and bigger your problem will become. Mold will follow. You cannot correct this problem without removing the tile and, likely, removing the wallboard material in the shower.

Your contractor installed it improperly and he should replace it. Check the rules with the contractor's board in your county. You are likely required to allow the contractor to correct it. You can't just have somebody else do it and bill the contractor.

If you hired a licensed and bonded contractor, the building inspector can pull his bond until the work is corrected. If you hired a craigslist handyman you may be screwed.