the reason the car creeped was because the parking brake was off, if it were on the starter (sulaff) would have burnt out (koyla marka sulaff bann jaata). The immobiliser doesnt have anything to do with this.
Even if your car had no immobiliser, the only relay shorting here is the starting relay - so the ECU was actually off which also means that the engine would have never started even if the starter was cranking.
I always tell people that "do not wash the engine unless you are 100% sure you know what you are doing" when I clean engines before working on them I make sure to protect important bits first and every brand/model has different requirements. Moral is that a dirty working engine is far better than a clean non working one.
e.g. I had a chevy venture van come to me with a constant crank sensor A fault which was not rectified after replacing the sensor, replacing the trigger wheel, synching it with the scan tool etc. The problem was a coolant leak which trickled into the crank sensor wiring essentially shorting it while driving. Stupid fault to diagnose - I used a flouroscent dye in the coolant to see the the leak in the dark. and I found it right on the connector.