Hey Joe,
You don't need to worry about how the hazards work, there is a separate wire for left and right indicators. It could be that the installer picked the feed wire from the flasher unit accidentally when he was testing. you just need to find where the connections are made and test. I'm not familiar with that alarm I only use Compustar and Viper, you may find a fuse blown from the alarm if it has two flasher circuits.
I normally trigger parklights unless the customer insists on indicators. Why would you not want to see those taillights flash!