Dave, the new style tire machines will clamp the wheel from the inside or from the outside. When they clamp from the outside, they grip the rim by the edge or the bead area where the tire seats up. They just have to release the clamp when puting the air in is all. You will be fine getting your tires mounted with one of these machines. The tires do go on from the back of the wheel. It is really not a big deal.
Russ
Russ