I have a pair of Neo-Gens that have been sitting in my garage for a while, and I noticed brown oily goo-like deposits on the inside of the tire (not on the inside sidewalls).
I didn't notice if they were there before unmounting or not.

What is it, and are the tires still safe to use? There doesn't seem to be dry rot, as the tires still look fresh on the outside.

 

Someone probably used fix-a-flat in the tire, or maybe got air from a compressor that had lots of oily goo in the airline.

 

Wash them, inside and out, and look for signs of dry rot or weakening/thinning of the material.

Pics might help others answer you, but I'm outside of my knowledge realm here.