So this accuracy claim is not saying that they engineered a clock that will only lose 1 second in several trillion years. For one thing that clock would have to

So this accuracy claim is not saying that they engineered a clock that will only lose 1 second in several trillion years. For one thing that clock would have to survive the sun going nova. Rather it's a statement about the width of the frequency they are measuring and their ability to divide that down to a second. They are saying that they have two clocks measuring the same frequency and have analyzed their dispersion against each other over a period of time and gotten this result. Long-term aging effects aren't going to change the frequency of the atoms (except new physics, but we can rule that out via observations of the Lamb shift in distant hydrogen), but things like gas infiltration, lamp aging, changes in laser characteristics can all cause atomic clocks to drift. This is pretty significant for rubidium which is why the lamps need recalibration periodically.