That's okay...that's part of cooking with wood. You are going to get a few minutes' burst of white smoke initially. If it stays white, then you have a problem - discussed and fixed in posts above. A few minutes of white smoke when you initially put on a fresh piece of wood is normal and won't hurt anything.
Remember, this is more art than science, and sound judgement plays a big part. If you are uncomfortable with the bit of white, then reopen the firebox door wide, or vent the smoking chamber momentarily. Don't ever forget this is YOUR food, and you get to cook it how YOU want to. No harm done either way, and if doing that makes you feel better about your smoke, then by all means do it. Seriously. You have to be happy with what you are doing, not doing something just because someone else is telling you to.
Wood is a challenging fuel to cook with. That's why they invented briquettes!
You should be proud to want to take on the challenge of wood smoking; once you get the hang of it you'll never want to go back!