DickWells, CapriRacer, I've used silicone when mounting tires for over 10 years on dozens of tires, and never once had one slip. That's not to say it couldn't happen if the air pressure got low, or you were running on a dragstrip.
I do watch my tire pressures closely.
Kestas, you can easily mount it on a piece of plywood, but I use it unmounted on a concrete floor. On alloy rims, I wedge a piece of cloth or shop towel between the tire tool or bar, and the alloy rim. This prevents scratching the wheel face.