Something tells me that the tree was not just dug. Fall digging (in our area) does not usually start until around the middle of October, usually begining with ash trees. I'm not sure when birch trees are dug.
However, if the tree was just dug, I highly doubt that an arborist would have planted it! Any self-respecting arborist would have either walked away from the job, or convinced the homeowner to wait until a better time. The only time I have ever dug a tree out of dormancy (or close enough to it) was 2 years ago. Big Jap. maple that either needed to be dug, or it was getting cut down. I did it, but didn't like it. I'm proud to say that the tree didn't hardly loose a leaf and you would never know it was dug in the middle of July!
With all this being said though, we just planted a river birch about 2 weeks ago. It too had yellowing leaves. It was potted (spare the argument, Mike, I know! I don't *like* to plant potted trees!) and we had bought it to use at a garden show this last spring.
Birch trees need a fair amount of water, especially this time of year. You will have a hard time over-watering it.
HTH.
Dan