Disarm setting off starter kill

I had a DEI Rattler car alarm installed a couple years ago on my '95 Nissan 200SX SER, and after about 3 months it started causing trouble with the starter kill.  Sometimes when I push disarm on the remote, and then try to start the car, it won't start, even after arming and disarming again.  The only way to get the starter to work is put the key in the car door and lock and unlock.  This all happened after one day I went to my car and hit disarm and it set off both the factory alarm and DEI alarm.  I even removed the fuse for the factory alarm, but still, the starter often won't work without putting the key in the door and lock/unlocking.  It arms/disarms fine now, but somethings setting off the factory starter kill I guess.  Anyone have any ideas on what could be causing this???   Also to note, they didn't seem to use any diodes in the installation which I've seen used in other similar applications. 

Last, NEVER go to Audio Express in Tucson, AZ!!!!  They're not called the home of the $1 install for nothing.  They'll break parts on your car and wire head units up with electrical tape and then deny it and say that inspecting the stuff voids your warranty, and you'll have to wait all day for a 1hr install, and then have to come back because they screwed up.  Also the worst customer service possible, after the point of sale you become invisible to these idiots.

Thanks for the response!  You're exactly right.  I'm pretty sure those turkeys just ran the disarm wire to the unlock and the arm to lock, totally forgetting the OEM arm/disarm.  I'll have to check it out today to be sure that's what's up.  I found from searching a thread on this topic over on the SR20 forum that you need to run 2 relays for these connections as well, which I know for sure they didn't do.