I would like to know where you obtained your definition. As far as I know you mix one primary and one secondary color, of course you've expanded this to include opposites on the color wheel. I can see where you got the idea.

Tertiary may not mean three colors (primaries) are included. I think it is more the third set of mixtures after secondaries that go around the color wheel.

As for primary and secondary, they mean yellow and orange, for example. Tertiary colors are not greys or 'neutrals.' I see "cough" that Wikipedia has a good description of tertiary colors if you are so inclined to look.