[shric]

> Isn’t the second defined as a specific number of cesium transitions?

Yes

> How can anything …

So your cesium counting device will fauthfully provide such a count and depending on their altitude it will be at different rates.

Both clocks are each experiencing time at the usual one second per second but gravity dilates spacetime.

Locally, a second is always a second, but from everywhere there is no such asbsolute, just as there is no universal "now".