I haven't seen that specific kit but I am almost 100% sure that you can define whether the signal is positive or negative. You have a wire that you feed the signal into (ie connect it to +ve or -ve), and then the unit sends that signal (whichever it is) to the existing system.
If you double check and it definitely doesn't have this facility then it would not be too difficult to use a NC ("normally closed") relay to do this job. A NC relay works sort of in reverse of a normal relay - when there's no signal to it, it acts like a switch that's on. When it's tripped, it OPENS the switch ie disconnects the circuit.
I am assuming your description "the negative feed to the locks is constant until its cut which trips the lock" is accurate, it sounds unusual but toyota wiring often is.
Basically, what you would do is cut into the existing -ve feed and put a normally closed relay in there. Then you would use the +ve signal from your new remote locking unit to trip that relay - when the relay sends a signal, breaks the negative feed.
You could also use a double-throw relay and disregard one terminal on it, eg
http://www.jaycar.com.au/productView.asp?ID=SY4070
What you would do is cut into your existing wire, and connect one side to terminal 30 and the other to terminal 87a. This restores the circuit you've just cut.
Then you would connect terminal 85 to ground, and terminal 86 to the +ve signal from your new central locking unit.
Those terminal numbers are right for the jaycar relay but may differ for other brands.
Again, this is based on your description of the existing system and I can't vouch for that one way or the other.
This is not legal advice.