Filling a 20 count humi is definitely enough to make the rh jump, if the cigars are coming from a high rh environment. Cigars that wet are probably impossible to smoke. It's possible that they came from the store like that, but if you tried to smoke one you'd've known immediately, and that would corrolate with a high rh in a small environment after putting them in the humi.
If it were me, I'd leave them for a few days, don't add water, and be sure to keep them 60-70F. The rh where you live says 45% right now, so that inside your box should come down. Keep in mind also that a smaller space is going to be harder to stabilize.
edit - BWA's suggestion to get a digital hygrometer is a good idea. When you realize you need something larger, go for the beads - very low hassle factor.
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