Atomic clocks measure oscillations in atoms... if every fundamental particle is slowed down by the same amount, then it cannot be perceived as anything else than time slowing down, as our conception of time is based on the speed which the earth orbits the sun, and therefore it is the rate of development of space. If everything is slowed down by the same amount of speed, then time is effectively slowed. It's true that conditions could affect radioactive decay, but the way any clock system is slowed by the same percentage suggests it is not just outside conditions.
More definitive, the fact that light travels relative to an observer at the same speed no matter what speed that observer is travelling at.. the only real way to explain that is time slowing down, when there is a 3rd party involved and the observer's speed and distance relative to this 3rd party are measureable.
The clocks are in their own independant time frame as always, which happens to progress at the same speed as that of earth, as they are travelling at the same relative velocity and under the same gravitational influences, though could be considered "Behind" by an unchanging amount, as their time was slowed for the duration they spent in orbit