We are all curious.
In defense of all concerned, electrical problems are some of the hardest to troubleshoot, and even harder without being able to put "hands on." Intermittent problems are some of the worst. Sometimes all conditions and/or symptoms are not provided or not reported correctly, because they happen so quickly, seem irrelevant, reported in non-standard terms, etc. I'm not saying that is the case here, but it is one of those things that happens.
It is like one person referring to a neutral as a "white" wire. Sometimes that is the case . . .with 110V house wiring, but the same wire can be used for 220V then the white will be another hot (though code requires it be marked with banding or paint at each termination). In the case of a machine a typical rubber SJ power cord will also usually have black, white and green wires. When used for 220V both black and white will be hot. But, depending on the cord, the hot leads could be black, brown, red, blue, etc. As far as motors, the internal wiring usually has numbers somewhere on it, either printed right on the insulation, or on an applied band. That is what you should use to wire it for 110V/220V and to change the direction of rotation. The leads from the start capacitor may or may not have numbers. I don't think there is any standard for internal motor wiring colors. The switch may have different colored wire all together. All bets are off if the motor was rewired.
Now, back to the original problem as described by Barbara- The double push of the off button is a still a puzzler to me. She never said if it was a mag starter or mechanical switch. This is a pure WAG, but if a mag switch is wired improperly (read really weird) it might be possible for the decelerating motor and the reverse EMF if generates to re-energize the contactor coil and attempt to start the motor again. Barb didn't say what the interval was between activations of the stop button.
Anyway, I'm dying to know the answers.