When problems occur I would call and ask the shop to check it out. I would not call and complain and start pointing fingers at the installation facility. This tactic probably will get you no where. I know when customers do that to me, I am less inclined to offer my help.
back on topic
ground and ignition is usually interchangeable. it just needs to see opposite conditions. if ignition post has 12 volt positive then the ground would be negative or vice versa.
grab a test light. while the car is off see what posts you get power.
you should get power 12 volt on battery 1 and 2. nothing on ignition wire and ground wire.
while the car is turned on, you should have 12volt power on only one of the small posts.
if you have power on one of the smaller posts while the car is OFF, then remove that wire. then retest to see if that post has power. if it does then relay is bad. if it doesnt, check for power on that wire that was attached to the small post. if it has power then that wire needs to be rewired to a switched 12 volt power source.
"thank you for calling tech support, please fill out the survey after this phone call"
LOL