Your alarm is not disarming correctly or at all. Whoever installed this did not test the system before giving you back your vehicle. Or did not know what the hell they were doing.

Your remote entry/ starter /alarm should disarm when unlocking the doors and arm when locking the doors.

I believe the alarm disarm shoud be pulled to ground (Chasis) and float when arm. This should be done with a didcated digital output from your newly installed system.