The correct way is exactly how its shown in the photo, though I do think that they are a bit too low, possibly maybe too big for the horse, and you do need to make sure that they are tight enough to not slip down. I knew a polo pony who wore those type of boots, and the owner didn't put them on tight enough and they slipped down around her fetlocks, and messed up her front legs pretty bad. I love PC sports medicine boots, used them on my dad's 35 year old gelding, and was able to do barrel racing, and jump over small jumps up until he colicked, and never had a problem. They are def. Easier than polo wraps, and offer a lot more support as well as protection for the legs than polo wraps, or even splint boots or jumping boots.
Yes, you can put them on wrong. Those boots are put on correctly, but I agree, they are likely too big for the horse. I'd go down a size and use those for hind boots.
I personally do not use any boots, except on schooling horses who are ridden more than once a day or jump. On my own horses, I never use boots, for riding or lunging/round pen work. But, I don't do barrels and my daughter only jumps ocassionally.