Baro normal behavior?

Is it normal for the pixhawk to read zero altitude when first powered up then steadily gain around 15 meters in about 5 minutes time? This is even if the gps gets a 3d lock in the 1st minute or so.

Anybody?? Also does the pixhawk consider itself at zero altitude upon arming or does it go with the baro reading 15-20M since powered up?

Yes, - barometric altitude is always AGL at point of start.
It could change a little due to temperature difference, or ast changing weather but not that much…