Stop in for a cup of coffee

Mine does not touch the wheel either. When it was new. But a new tire can cause things to happen.
Cant think why a tire shop would have a different machine for mags. They should have plastic guards to prevent marring. If they do nothing but tires they will likely have the latest and greatest im hoping.
A lot of the shops around here still have several old hub and bar machines to do steel wheels and only one that does modern mag wheels. It depends on the store and how long they have been around. That why when you have a nice steel wheel, you need to ask for the mag machine if you want it done without wrecking the paint on the rim edge.