From what you describe it sounds like your ESC is programmed for a Heli where the high inertia of a rotor requires a slow start up to prevent overloading the motor and the gears, however according to the instructions the E-flite 22 amp BL ESC is a 'simple' type and does not have this feature! This is a puzzle?
The motor will get warm but should not get hot too quickly particularly as in the mini Ultra Stick it is right in the breeze out front.
What prop does it have on ?
Too big a prop will over load the motor it will then get hot and eventually burn out!