Yep - the 'orange gene' is just the gene that completely blocks all production of eumelanin pigments - blacks, browns, cinnamons, blues etc, it's not a gene for red pigment to be added to the coat, it's a gene for black/brown pigment to NOT be added to the coat.
A black cat produces eumelanin (which is really a very dark brown, there's no such thing in nature as a true black pigment) and phaeomelanin (which is yellow, orange, or nearly red pigment depending on the density). The black completely covers up the red in a solid black cat. A brown tabby also produces both, and the red pigment shows through as buff or yellowish or reddish colour where the hairs are banded, but doesn't show through on the dark stripes/blotches causing the tabby pattern. A red cat just doesn't produce the black/brown pigment at all. All coloured cats produce red pigment (in varying quantities and shades), but depending upon the amount of black/brown pigment it produces and in what pattern, it will either show through in varying shades or it is covered up by the black.