It sounds like you have the alarm programed to be a passive arming system, you should be able to turn those options off. And just a reference for next time, You shouldn't have to run any wires to the battery, all of the wires that you need to install an alarm on a 2g eclipse is under the ign. column. The yellow wire is just a starter interupt, when the system is armed the relay is opened and the starter wire is broken, when the system is disarmed the relay is closed and the car will start. This is why I only recomend an alarm made by DEI, their customer service is top notch and their alarms are some of the best.