Not all acylics are created equal. (For that matter, neither are enamels.)
The acrylics you tried are intended for use on a porous surface such as paper or cloth, they are not formulated for plastic. Some of these will bond well to some "plastic" or similar surfaces, and some will not. Acrylic model paints will give you much better adhesion.
There is, however, something else: Plastic surfaces painted with acrylics must be much cleaner than those painted with enamels. The reason for this is that the solvents in enamels will often dissolve surface contamination such as skin oils and mold release agents. Acrylics usually use water or alcohols as their solvent (often with other cosolvents and additives). These do not dissolve the more common surface contaminants.
For that reason, plastic surfaces to be painted with acrylics need to be thoroughly clean. Detergent and water, surfactant cleaners (Formula 409, Fantastic, Windex, etc.) or specialized cleaners (Simple Green) all work well. Just be sure to rinse and dry thoroughly! I often follow these with an alcohol wipe.
Wearing latex or nitrile gloves while handling and painting the clean model helps, and it keeps paint off your hands, too.