Try it on a scrap piece of plastic, to see if you can re-create the problem. Do you hand-brush, or airbrush?
First, lay down a basecoat of MM acryl, then give it 24hrs to fully cure. Try the tamiya thereafter. If you're hand-brushing, I've had similar problems, where the tamiya paint will actually LIFT the MM from the plastic. I think that's just due to the strong medium. I personally avoid hand-brushing tamiya paints like the plague, as IMO they just suck for handbrushing..
If the paint beneath is FULLY cured (if not 24, give it 48 hours just to be sure), airbrushing tamiya acrylics over it shouldn't be a problem.
Let us know how it goes.