Bugs keep popping up in my salt cellar?

It's a shame that there's no photo of the critters. That might help some people here decipher your mystery.

Since I have left salt (both kosher and sea salt) on my kitchen countertop for decades without this problem, my guess is that there is something different with your situation.

There's always the possibility that someone is introducing a contaminated utensil into your salt cellar thus leaving foreign food particles that might be attracting insects (a.k.a. "double dipping").

There's also the strong possibility that someone with unclean hands is leaving food particles on the exterior of the salt cellar while holding it.

You will have to think carefully about how the various people in your household interact with the salt cellar.

For my kitchen salt cellar(s), I use a dedicated scoop that stays with the cellar. I periodically use my fingers to pick up some salt but only if I know my hands are scrupulously clean (I live alone). I will periodically wash the container (and scoop) regardless.

It's worth pointing out that I leave the side pouring flap of my Diamond kosher salt box open and I've never found any insects when I poured out the salt.

I've never had any problems when I put out little dishes for salt at my dinner table (typically these are old oyster shells).

And lastly I keep a shaker with sel de Guerande around the kitchen. The revolving top reveals holes of different sizes but it is always in an open position.