Yes time is slowed down for them, and it has been proven mathematically, and supported physically. They go much slower than the speed of light, and for light to get to Earth, it takes Earth time 8 minutes. Like I said above, without time dialation, they would decay completely in a matter of seconds. And, travelling past the speed of light reverses the time for you, not for Earth. One theory which explains this concept is as Dan described above, infinite realities.

@ROMAC, well, not sure if I would want time travel to be invented, but with this concept it would allow people in the future to migrate to other planets (similiar to the american colonists in the 16th/17th centuries). It would allow you to travel 50 light years and age only a small fraction of that. Rest assure that people who leave will not return to Earth, as everything would be long gone by the time they got back.