The Basslink can be installed with or without a remote wire meaning...
Normal amp installs have a battery, ground, and remote connection. Amplifier turns on and draws power only when the remote wire is powered up. Most installations would have the remote wire connected to an amp turn on lead at the radio, or if that isn't availible, then a switched accessory wire.
Now the Basslinks with the auto-sensing feature, you're not required to run a remote wire. The unit will power on when it detects an audio signal at its input. Neat feature for a non-professional installer who wants to put it in theirself.
I'm guessing they did one of two things with your install... either hooked up main power (normaly goes to the battery) to an ignition source and used the auto sensing feature or ran the remote wire to an ignition wire instead of an accessory wire. The accessory circuits stay powered in all key positions other than off and start (while you're cranking) versus an ignition circuit which is only powered during the on and start positions.
Either way, it sounds like they went through more trouble than they likely had to... I mean from an installers stand point adding and amp to the factory audio system in a car like ours is about as easy as it gets... even more so when you use the auto sensing feature. Make them reconnect constant power to the battery, you'll probably have to buy a GM side post battery terminal for a few bucks and run the remote wire to an ACCESSORY circuit.