A Transparent Girl with Visible Thirst - Ch. 6 - Accidentally Pervert

[Xelarion]

The quick and dirty answer is that "invisible" people have a secondary periphery sense that acts on their eyes allowing them basically a somewhat accurate sense of their own physical body. Something similar to seeing the outlines of your body and your own movement, but the core space is filled with the physical distortion of your mass acting on the space where your body should be.
No, just being there doesn't immediately allow you to see through a transparent object, otherwise clear glass would never have accidents for both animals and humans.