They do give you plastic anchors to put in the sheetrock. With mine I had rebuilt the bathroom and had added a backerboard under the sheetrock. This made it very secure for my 90 year old father who keeps falling.
I did not use mine in the tub. I used mine next to the toilet. So far no issues in that location.
On one I used the back side of the wall which didn't have tile and then measured. On another I couldn't do that so I had to very very carefully drill a hole through the tile layer and then very slowly drill through the composite board by hand until I could fit a tiny wall camera inside. Once I did that I knew just how far I could go either way without hitting something critical. I used drywall mounts though as to not make any more holes and the bars were exceptionally strong. Almost as if they were in studs.
yes they are