Yes, while hard to diagnose over the internet, an electrical issue is by far the most likely cause. Things like stuck contacts in the ignition solenoid, bad ignition switch, back fed 12 VDC to the ignition circuit, etc.
That is why "what else is working as it should/not working as it should is a good place to start. For example if other things that should only work with the ignition on do not turn off (Allison shift pad, dash HVAC fan, etc) you have pretty well narrowed down the problem.
But we do need to OP to get back to us with this information!