I can't find anything in the FAQ or rules that clarifies when this happens. The timing is really only important to determine if you can play the card you draw because of the icon to add icons to the action you are doing.
For instance, I play a desert terrain card for 1 movement point and a card draw. I draw air cavalry. Can I play it to make my movement points for the action 4? Or do I have to wait for another action?
The rules imply that you play cards to gain points to do a single action type. It seems like you don't interleave card play and spending the points until you are done. But I don't know if this is true.
This is not spelled out explicitly in the rules, but my understanding is that the drawn cards cannot be added to the current action, as the bonus is gained after your action is completed.