You're original post wasn't clear as to whether the remote start is OEM or after-market. Given what you've described, I suspect it's the latter. In order to function with the keyless system, some after-market remote start units require a keyfob be left in the car to work. If this is the case, your car is starting on it's own due to the presence of a keyfob inside your car, and there may be a problem with the units wiring.
If it's the factory installed OEM remote start, I'd say a trip to your local dealership is in order.