How do you avoid cracking or webbing in fresh car paint?

I would say it was your prep work that caused this. I'm not a painter myself but I've been around paint booths long enough to learn some stuff. They cracks you have are known as spiderweb cracks usually attributed to too much hardener in the paint. The paint dries and hardens too fast that it develops surface cracks much like when it rains and the dirt dries up too fast that the top surface cracks. However, I'm assuming you didn't mix any hardener with the primer, but you did wipe the surface clean with lacquer thinner and glass cleaner. When left on the surface, it helps dry the primer that much faster. The surface should only be wiped down with water and a sponge or lent free cloth.