the 360/One controller are the same so they layout will be the same. The only way you can know what the mod/plugins use is by reading the config file (it'll have it listed there). As for the page you linked it goes as follows.
DPadUp - Directional Pad Up
DPadDown - Directional Pad down
DPadLeft - Directional Pad Left
DPadRight - Direction pad right
Start - Start button (obviously)
Back - Back button (obviously, located on the opposite side of the start button)
Left Thumb - Left analog stick
RightThumb - Right Analog stick
LeftShoulder - left "bumper" button located above the left trigger
Right Shoulder - right "bumper" button located above the right trigger
Then A,B,X,Y are self explanatory
And yes, You can use a controller with your mods. All (if not most) of the LSPDFR mods are compatible with a controller