a good controller should NEVER run when connected to the battery,
no matter what throttle signal is being fed.
So, my assumption would be..
that is not an EV controller at all but some cheap home appliance controller (fan, pump, whatever)
I must admit there are terrible EV controllers that might not be reliable here,
but you've already been advised to check the throttle signal, so that'd be covered

Oh one thing: many EV controllers DO NOT allow a potentiometer as a throttle signal, so depending on that make sure it's a true ratiometric hall effect throttle you have.
would you mind posting pictures?
that'd help identifying faulty/unsuitable parts and possible issues much quicker.
'sid