It's a tight squeeze. The TP roll will rub against the cabinet (or wall) until you've used a few layers of TP. Since PT rolls are much narrower than past product, there is plenty of room, almost to much, as you find you will have about 2" of extra space for the TP roll to slide side to side.
I installed mine with 5/8" #8 wood screws, just to make sure the TP holder didn't loosen with repeated use.
The outer finished posts and bar on the Ladera toilet paper holder #BPH-LR0C are made of Zinc metal. The mounting brackets and screws are made of steel, and the anchors are made of plastic. The installed paper holder projects 3 7/32" from the finished wall. Below is a link to the specifications of this model for further details: https://pfisterstorage.blob.core.windows.net/documents/ss-bph-lr0x.pdf