ActiveResponder95

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

Early access loyalty rewards programme info is in the post below this one, please scroll down.
 
Download Assorted Callouts HERE: http://www.lcpdfr.com/files/file/9689-assorted-callouts-0032-petrolgas-theft-pacific-bank-heist-traffic-stop-backup-required/
With Assorted Callouts, my aim is to provide a varying experience, adding a range of differently-styled callouts for you to experience. They all have one thing in common, though, and that is a fun and sufficiently realistic atmosphere.
Currently released:
Petrol/Gas Theft Bank Heist  Traffic Stop Backup Required Stolen Police Vehicle Person with a knife Solicitation Organised Street Race Illegal Immigrants in truck Store Robbery  Shoplifting Hot Pursuit - x16 Currently in progress for the next release:
Collaboration with @FinKone's Repeat Offender callouts. [On Hold] Mugging in progress. Currently planned - ideas I like:
Excessive Noise Complaint Drug Deal - ambient event. Callout suggestions are welcome. Latest development update:
 
  All of the above information is subject to change but is a good indication of what is to come. By posting this, I haven't made any commitments to the contents of Assorted Callouts. Currently Known Issues:
 

When you launch GTA V normally and go in game, Rage doesn't open at all?
 
Take a screenshot of your GTA V directory, please.