In 'the old days' (with 27Mhz etc. transmitters) it was standard protocol to turn on the transmitter before the car is on and turn it off after the car is turned off for this very reason, and in case any other signals were transmitted on the frequency nearby.
So this I guess would be the first thing to do. As far as my knowledge goes, most (competition) ESCs are programmed to stay completely idle when the transmitter is turned off first, or even to turn off when the car does not detect its transmitter signal for five seconds.
Maybe it would help to check that all trims are neutral on the transmitter and calibrate the ESC again; otherwise I would contact the manufacturer about it. They should know
