Logically, looking at the last thing to change before the issue arose is the best idea, at least in my mind. I would have them make sure that the power they used is not on a shared circuit with the security system (using the same fuse, wiring, etc.) Vehicle stereo systems usually have one power feed that is tied to an 'always on' circuit, as do security systems, and if they spliced into the circuit for the security system it could be doing something that trips the alarm.
Ideally, any stereo install in a modern vehicle (and I would consider yours modern) will utilize the factory wiring harness, but not every installer will do that - some will cut off the factory plugs and do their own thing because they feel that this is 'better'. The problem is, the word 'better' is very subjective. Your idea of 'better' and my idea of 'better' may mean two very, very different things
If these systems are using separate circuits have them disconnect the stereo fully and then test the alarm again to see if it still behaves the same way. If so, you know that ~something~ related to the stereo is the culprit. If the alarm still acts up it does not necessarily rule out the stereo - you may have to have the dealer (or an auto electrical specialist that you trust) verify that the stereo installation did not harm any wiring. Just because the stereo is now fully disconnected does not mean that something they did during installation has not damaged some other system. In order to rule out the stereo and installation completely you'll probably need to have someone who is certified/approved/etc. to work on your alarm system check all of it's systems and verify that it has not encountered a problem.
Electrical issues can be tricky, but they are far from impossible to resolve. You just have to be very methodical and document each system, each test, and each result clearly so that you can rule out one thing at a time. Make/accept no assumptions in this process, do not try/allow shortcuts, and if you have others do the work try to get the most qualified people you can.