I think I know what the deal with the tach-off function is. I think that the remote start uses the tachometer (if the car has one), to know when to stop cranking the starter. Otherwise, it either cranks for 8 or 1 seconds, depending on the selected setting. Also, I think that when they install the module they sync it up to "learn" your car's tach instrument. So, I'll bet that when you turn it to off, the car is chirping because it has learned your tach but now you're telling it that you don't have one. I'd imagine the error code might go away if you force it to un-learn your tach or reset it and start from scratch with no tach.
Dont know if you already know all of this, but that's my guess as to how our remote start works.