Not necessarily - but if the shop won't let you stand there and make sure they get them on right, go to another shop. Note in the wheel photo below that there are ten holes in the wheel; the five small ones are for the steel drive pins on the hub adapter to fit in, and the five large ones are clearance holes to accommodate the lug nuts that hold the adapter to the hub. If you mis-index the wheel 1/10th of a turn, it won't seat on the hub, the spinner will only catch a couple of threads on the adapter, and the wheel WILL come off. NOBODY in a tire shop knows this.
The other small photo is the mating hub adapter, if you haven't seen one. The five drive pins go in the small holes in the wheel, and the holes are for the lug nut studs on the hub and the lug nuts that hold it on. The one in the photo is a reproduction and has the slots for the safety pins, that match slots in the spinner; originals (and some early reproductions) don't have the slots in either part.
The third photo shows the K-H and D-49985 cast into the back of an original GM wheel; if your wheels don't have this or have "Western Wheel" cast into the back side, they're reproductions.