Sounds like wood mites. These will not harm your cigars but are a pain in the arse. Best bet is to find the the box that they are in and just take the cigars out of it. Vacuum the box and then let it sit empty in the sun during the day as the UV from the sun will kill them as they don't like light. These are usually associated with moisture / high humidity and since you mentioned that your room gets really hot during the summer is probably your cause so adjusting these will alleviate the problem. They are after the glue in the boxes and in the bands.
If that doesn't do it, you might want to empty your humi and vacuum it with a crack & crevice attachment.
Brush your cigars off but you can also place your cigars in the freezer and kill any that are still in there. You don't have to deep freeze them like with cigar beetles which require extremely cold temperatures for a prolonged amount of time. Personally I wouldn't want to freeze my cigars and would go the vacuuming route.
Also check inside your humidity device as they might be in there. If that's the case I would clean it out or replace it. If you're using beads just replace them.
Hope this helps.