Antimatter particles follow the same laws of physics as matter. The reason that it is assigned those particular values of charge, spin, etc. is precisely so you can use the same set of physical laws.
Take the example of an electron and positron moving through a magnetic field. You will find, observationally, that they curve in opposite directions. I suppose you could say that a positron has an anti-negative charge and accompany it with an appropriate reformulation of E&M, but it is better just to say it is positively charged. Additionally, there isn't a difference between the positive charge of a positron, and the positive charge of any normal matter particle, so there is no reason to call it something else.
However, antimatter particles don't always behave oppositely to matter. Consider mass and gravity. Both matter and antimatter have conventional, positive masses, and as such behave in exactly the same way when it comes to gravitational forces.