It is crackling because you are placing a fast drying paint (acrylic) onto a slow drying surface (primer). This to me indicates you are using an oil based primer and a water based acrylic. Some acrylic enamels will dry over oil based primer and some, as you've found, do not. Since you cannot rough the plastic surface of the figures before applying a primer, you should use a water based primer and then an acrylic enamel paint. The enamel will have less of a tendency to crinkle because it is a hard drying paint.
and read the "Differences between acrylic and oil paint" article.
Another possibility is that you have come across a paint manufacturer who uses the same labeling for water based colors as it does for oil based products, allowing for someone to pick up some oil based brown with the other waterbased colors. The labels must be read. Sometimes the oils of a primer will coat a surface and prevent an acrylic from adhering thus allow floating plates of dried material (crinkles).
Then I found this paragraph under "Primer (paint)" in wiki, and note the part about "for plastics... are not water based..." and make a decision to switch to an oil based enamel for your final coating
Primers for plastic
Using a primer on surfaces made of plastic is only necessary when making a drastic change of color (going from dark brown to white, for example), because most household plastics are not very porous and are not easily damaged by moisture; or when a long-lasting coat of paint is desired. A primer will reduce the number of layers of paint necessary to completely cover the previous color, and will help the paint make a thorough bond with the surface being painted. Because most paints and primers designed to be used for painting plastics are not water based, an important point for choosing a primer for plastic is making sure the primer's propellant or solvent will not dissolve or warp the plastic part itself (e.g. most common household spray paint will damage polystyrene foam). Both the primer and paint should be tested on a small hidden spot of the part being painted.
So, from what I've read, you really shouldn't need a primer on plastic (just be sure it is chemically clean and dry before painting). Primers are either oil based and shouldn't be mixed with acrylics or they are LATEX (a rubbery material) and are not a good base for a hard acrylic coating. Or, you should just go with an enamel (like Testors) on the plastic pieces. Testors paints have been used by makers of plastic model cars, boats and planes since plastic models have been around. I do not work for Testors but have used their product for fifty years successfully.