"So it adjusts automatically the measured pressure at a fixed altitude ? Well, maybe that is not as good. My altimeter is also being used as a weather evolution instrument and a change in pressure at a fixed elevation, might show how the weather will evolve."
No, I don't think that's quite right.
The Core simply intuits whether or not you're on the move and assigns pressure changes to either the barometer or the altimeter accordingly.
Once you stop at camp, for example, it notices that the pressure hasn't changed (beyond some small tolerance) for something like 12 minutes and switches into barometer mode. From then on, pressure changes get logged as changes in the barometric pressure. So you can most definitely evaluate possible weather changes–the watch even has a storm alarm.
When you start moving again and the watch notices enough pressure change (in about a 3-minute period) to prove you've changed elevation (i.e., the weather can't change that fast), it switches to altimeter mode and begins assigning all pressure changes to elevation. It switches back and forth between modes as you hike and/or stop.
It sounds gimmicky, but works amazingly well. Of course, it can't know what to do when you're changing elevation *while* the weather is changing, so all that gets assigned to the altimeter and calibration does drift. You can also lock the watch into either barometer or altimeter mode if you want to take manual control, but I find the auto mode does a great job of minimizing the need to recalibrate.

