Although a properly calibrated digital hygrometer may be more accurate, there is nothing wrong with the analog style. They have been in use for many years before the digital ones became available recently.
1) overnight is not long enough for a proper salt test. You need to leave the hygrometer at least 24 hours.
2) To check the seal on your humidor lift the top about 4 inches, then let it drop. It should not slam closed, rather the air should kind of make a "whooshing" sound. You can use a flashlight inside to check for gaps or use a dollar bill around each edge, it should be tight all the way around. If you find a spot where the bill just slips out easily you can use a small piece of masking tape to help make the seal tighter.
3) After seasoning, put your hygrometer inside for 24-48 hours it should show a fairly stable reading.
4) Just a few sticks in the humidor will be tough to maintain. As you fill it up it will be more stable. When its mostly empty, the humidified air will escape each time you open the top.
I see no reason to suspect either the humidor or hygromter at this point. Dont give up, it may take a while to get things perfect. You can keep your cigars in a zip lock bag or a tupperware type container for several weeks. Just open it up every couple of days to get fresh air inside.
