What could be the reason? It looks like there is a kind of tension in the steering system released after engine is started. It just gives short jerk of wheels and the steering wheel and later everything looks just fine.
bye
pentaq

 

Do you have an automatic? maybe use your emergency brake to reduce any long term damage... until you figure out why its jerking.

 

This happens in my car with manual transmission.
pentaq

 

i thought it was because the power steering pump is getting pressure

 

I'd check all the motor mounts.