The purple stuff tends to have a water resistant coating on it, but the guts are still gypsum and you'll be poking holes in it to attach it!
CBU won't be damaged by being wetted. To get the surface prepped, consider setting mud versus the premixed stuff. YOu don't have much time to install it, but it won't soften again if it gets damp like the premixed stuff. Mix small batches.
FOr reference, I'd take a level and check the rim of the tub. It should have a slight slope to it into the tub and not slope outside. It could just be the shower curtain isn't well positioned, or the door, if it's configured that way, but more often than not, it's the tub was not leveled properly during installation.