You can use their dark wash over Tamiya acrylics with no problem whatsoever. They actuallly recommend using their products over Tamiya paints. I use them all the time over my Tamiya-painted tanks.
Their pre-mixed washes are of an enamel-carrier type. Regular mineral spirits will remove the excess. MIG's washes take a little longer to dry, and dry to a semi-gloss finish. Most people though would tell you not to use black/browns for panel lines on cars; I've heard that a darker tint of the body color is actually best.