Altitude jumping while sitting at home

The "during activity" setting is not important as, as you said, you were doing no activity.

What's the setting of "not during activity"?

Its "off", sorry, should have been on the screen shot

Almost every watch with a barometer I had started doing this. In the beginning, they are rock solid. Only report altitude changes when I'm really going up/down somehwere (stairs, walking up/down a hill, whatever). After a while, they start acting up just like in your screenshot. I can sit on my couch for an hour and get credit for flloors I've aparently climbed... (my FR945 does this even when setting the mode from automatic to barometer. The height will remain stable, regardless of height changes, but I still get floors credit when sitting or lying...).

My guess is, that it has something to do with the barometer hole. I clean my watch regularly while showering and blow the barometer hole free of water afterwards. Still it happens after some time. I had to RMA almost every watch because of this. I figure, if the watched isn't cleaned regularly, the problems starts sooner because of all the gunk that gets clogged in the baro hole. But again, that's just my guess (after some experience with several watches that had a barometer).

Thank you. I wonder if Garmin would still care given I bought the watch 1.5y ago.

Warranty in Europe is two years. I just had my watch replaced by Garmin UK after 15 months from purchase for an unrelated problem. 

The auto-calibration not during an activity is only done overnight during your normal set sleep time (and when connected to a phone with GCM running).

Check if the watch is in "altimeter" mode. It reads any change in pressure as a change in altitude.