It's the same with the DL tag - the NA tag will stay on the player until the moment when they actually start to play again for their team. He is scheduled to play tonight, so I'd move him into your starting lineup now, so you don't miss out.
Steven is right, regardless of the status, you can place him in an active roster spot and get credit for his pitching tonight.
All player status' are updated overnight, but update requires that they actually debut in an official MLB game. Cashner should have the NA dropped by tomorrow, but that doesn't prevent you from starting him today!
I was able to start him, but because his eligibility was NOT updated, I was NOT able to start him in a Starter spot, which cost me innings from one of my bullpen guys. Little bit butthurt about that one.
So far he only has 2 game starts this year. As soon as he gains his third start (likely tonight), we will update his status overnight with SP eligibility. So look for the SP tomorrow, and have a great 4th!