Yes, you seem to have a bit of a problem, and if it weren't for the photo's I wouldn't have been able to know what you were talking about. So first a bit of a glossary.

Wheel refers to the entire thing, including (working from center out) the hub, spokes, rim and tire. In some cases it might refer th the entire wheel without the tire, as in when you mount a tire onto the wheel.

Your brakes should touch on the rim and rim only, not touching the tire at all, and not hanging below the rim either. If you continue to ride with it as it is, the brake shoe will cut through the tire causing a blowout.

If the bike is fairly new, and was set up this way the shop did sloppy work, and I'd go back and ask them to correct it. Otherwise, you and loosen and reposition the shoe lower. When you do so, trap a piece of cardboard, or a rubber band under the rear of the shoe holding it a bit off the rim. This will create toe-in and prevent brake squeal.

BTW- and this is important, before you start, if you removed the wheel, it's just as possible you didn't put it back all the way up into the fork, so before moving the shoes, stand the bike on the floor, open the quick release jiggle the wheel to settle it home (gravity pushes the fork down onto the wheel), then adjust and close the QR. Now re-check the show height, and correct if necessary.