I have seen them fail, and never seen oil in them. Doesn't mean they don't have oil in them, but the chances are very slim. The one that does is shown in the picture above. Notice how it has a metal housing for it. This is because the rubber flexes, and micro cracks, and if they filled it with oil, I don't even see how it would benefit the design. There is about a 1 percent chance there is fluid in that mount. That just just because I haven't actually dissected it.
Could the oil you see be coming from when you cleaned it, and it pooled somewhere, and discolored from the rubber, and finally got squeezed out after flexing? LOL. You never know. Touch it and rub it in your fingers. Is it water or oil?