No clocks use nuclear decays, this is a common misconception.
Some (not all) satellites use atomic clocks: They use transitions between energy levels of atoms (not their nuclei) that can be induced when they are hit by radiation with a very specific frequency. You can measure the frequency when that happens and you know one second has to be x times the period of that radiation.
Satellites that don’t need their own atomic clocks can get their time from GPS signals, from their own less precise clocks, or from ground stations, depending on what works best for them.
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