Again, the effect is different based on the material construction.
The “aging rate” of ceramic capacitors is how much capacitance they lose over time. It applies more to Barium Titanate (Class II and III) dielectrics than it does Class I (especially those made with Calcium Zirconate.)
When barium titanate is exposed to its curie point, the molecule changes shape. The orientation gives it a higher permittivity. However, as time passes, the molecule relaxes and causes the permittivity to drop.
So, the effective capacitance drops over time. It is a logarithmic scale. A few percent after an hour. Then another few after 10 hours. Then 100 hours, etc.
Murata has some FAQs with good pictures (but not a good way to link to them): Search Result | FAQs | Murata Manufacturing Co., Ltd.
Unlike other ways “aging” gets used, this change in the ceramic material isn’t permanent. As you found, if the capacitor is exposed to its curie point again, then the aging clock resets.
Regarding Polymer-Tantalum, their construction doesn’t have the same kind of effect. Their parameters change over time but not because of a natural effect like Barium Titanate—instead, the polymer oxides which increase their ESR. Or the Tantalum can crystalize and puncture the dielectric layer. Both of those changes are accelerated with energy, especially heat energy. So, Arernius works very well in their case. And it is where the operational life is estimated in the 1,000+ year span.
And for a third comparison. Wet (traditional) aluminum electrolytic capacitors also have an effective aging rate. In their case, the rate at which the electrolyte is consumed “ages” them. (And, coincidentally, during manufacturing, al-electrolytics go through an “aging phase” where voltage/current is provided to allow the dielectric to self-heal.)