How Mike did it seems very hard and creates an oversized package. I shipped tires several times, and the way I did it was similar to what "worker's" picture shows. Just use regular packing tape to bind two tires together. Shipping them as two packages of two tires should be cheaper than one package of four tires due to the size.

I just tape the two tires together by running loops of packing tape at 3-4 places around the perimeter to make sure they are securely together.

It is extremely unlikely that tires packed this way or any other way can get damaged during transport. You're buying insurance in case the package is lost completely. Insurance with UPS and FEDEX costs only a couple of dollars total for a set of tires.

The cheapest way to ship tires for me has always been through FEDEX Ground service.