I'd double triple confirm all the above.
Tires on a bike may be different than tires on a car, but tires in general all have tread patterns designed to grip road surfaces, while dispelling anything that would cause the tire to lose traction with the road - like funnelling water away.
Particularly in the sense of water, I could see a tire mounted backwards pulling water under the tire rather than pushing it out from under the tire, and hydroplaning on a motorcycle... I don't ride in the rain, but that doesn't sound safe.
From mounting my directionals on the incorrect corners of my car, I can tell you that they will pull, they are noisy, and are dangerous on anything but a clean, dry road surface - and even still I wouldn't want to bring them up to their rated speed.
Now, if the tire is ENGINEERED to be run backwards on the front - that certainly would be a different story. In that case, I'd expect to see not just a directional arrow, but one with "front" and "rear" designations like the tire Tom shows above.
If you don't see that special designation - I'd have the shop put them on right. It could be (like most shops), they've got some kid doing the menial work in the garage, and he just slapped the tire on between Facebook posts on his smartphone.