Hey, I have littermate brothers with the same thing! One does have herpes, but the other doesn't have a problem with that. The one with herpes LOVES to have me dig the junk out, but the other one hates it! I do it anyway, of course!
Tears naturally contain a substance called porphyrin, which is a pigment. When the tears dry, they leave behind reddish-brownish "eye boogies," as I call them when I'm trying to pry them out of my cats' eyes. The tear ducts are right there in the corners of the eyes, so that's where the junk accumulates. There is also probably an issue with tear drainage, perhaps congenitally small tear ducts; this is likely the case with Persian cats and pop-eyed, smush-nosed dogs. Chronic inflammation results in scarring and this may also affect the tear ducts. My herpes cat seems to produce a lot more of the goop than his brother, and it's wetter, so I think herpes is a factor, though not a big one.
Breeders of little white dogs (like toy poodles) have a lot of supplements and products that they swear by to prevent that stained look; I'm not sure that any of them work that well. However, raw diets (homemade or commercial) are reputed to get rid of them.
So all-in-all, yeah, chill, just keep them clean, and if I find out more (I have a friend doing a survey on the dog products) I'll let ya know.