What should I know before having bathroom fixtures installed?
Sounds like you pulled out some butterfly anchors instead of unscrewing them, or even large molly type. 

What I do in situations like this is to install a decorative BOARD behind the towel rack or toilet paper holder, on the surface of the drywall, which screws directly into studs. This can simply be a piece of 1X4 with routed or finished edges, or baseboard or crown molding in 3 inch or larger width, painted white or the wall color. If desired, continue around the room at a single height, making this look like a standard feature similar to the top of chair rail decoration.

Install this with screws long enough to reach into the studs behind the drywall, I typically use 3 inch long self drilling screws. If you don't want the screw heads to show, spackle over them or use caulk before painting. The baseboard or molding typically can be found in 3 inch or larger widths, cut to length as needed, providing enough room to install the racks or fixtures on it. The racks can then can screw into this. This eliminates any unsightly holes or bad patching that might be present, as the board goes right over them. Studs are typically 16 inches on center, use a stud finder to locate them. For the toilet paper holder, if the board is attached by screws into one stud firmly, and the other end is installed with butterfly anchors, it should never come off the wall.

The exception would be a block wall behind the drywall, which probably would have furring strips holding it up. You'd then be able to use a drill and concrete anchors with longer screws to hold up either the board, or the racks themselves.