If it's really an altimeter than steps "climbed" when not "climbing anywhere" is actually normal.
You see altimeter really does not exist. Altimeter is simply different way to show barometer changes. (As you can probably guess altimeter will be impressively accurate as long as weather does not change "on your way up" and hence the reason why Microsoft uses it : they figured it's unlikely that weather will change while you're climbing set of stairs)
Google "baro changes vs altitude" and you'll understand...
So if you sit still and weather gets worst (in general - but not always , this means that baro goes down) you'll see stairs climbed even thou you didn't climb any stares. What actually happens is this:
1. Baro goes down
2. Your altitude is calculated based on Baro reading
3. System new your "last" altitude and now it gets "higher" altitude because of the lover baro reading
4. Steps climbed just went up
Ho much of an steps climbed will you see if "baro goes down" depends on baro accuracy and frequency of sensor readout.
Most wrist devices these days are accurate to within 1m but older bar sensors were only accurate to about 5m.
So in other words if you just sit around and all of a sudden you see 100 steps climbed brace yourself, heavy rain might be just around the corner.
(sudden baro drops over short period of time are good indicator of an upcoming storm. For example this is precisely how "storm alarm" works on devices like Suunto Core)
EDIT:
The only way I can see that this can be remedied is if Microsoft Band start doing this:
1. Baro changes! Is user climbing stairs or is weather changing?
2. Check the phone weather station baro reading to figure out if band is really climbing or no. Use this to decide if the "stairs climbed" should be shown / calculated or not.