I just ordered an Autopage RF-420LCD to put in my other vehicle. I am going to use the wires that were existing for the factory Honda alarm, plus run my own for the other features not available with the factory alarm. Assuming your aftermarket alarm was wired properly, you "should" be able to use the existing wires.
My only concern would be if your "professional" installer used crimp on connectors. I have a personal hate of those crimp on connectors because one of them ALWAYS seems to cause problems. When I installed equipment 15 years ago, my employer insisted on using those awful crimp on connectors, yet when I did something on my own time, I always used solder and heat shrink tubing. My former employer always had issues from his "lifetime install" warranty and failing crimp connectors, whereas I NEVER had someone come back to me with a failed solder/heat shrink connector.
Sorry about the long installer rant. I haven't installed since graduating from college and starting my "career". It still pains me to see top dollar being charged for local installs, when the installs themselves are sub-standard!
Maybe I will buy a 2016 Mustang GT, maybe not...