Any idea on how to prevent rust on tea tins?

Honestly, if it’s a used tin, just toss it. Invest in tins meant for longer term storage, such as stainless, enameled or cherry bark, or porcelain storage caddies.

I think moisture is usually needed for rust to form. Are your tins getting wet? You can probably treat small rust spots by scrubbing, drying and applying a barrier like clear nail polish, but I’d only do that on the outside where the tea won’t come in contact with the polish.