No. The gloves are primarily to protect the nurse. And as far as "reporting people", I'm not a happy camper with that either, since you have suffered no harm. I am a big fan of the motto "mind your own business" unless there is a clear life-threatening situation. In the test there is no contact whatsoever with the glove, the needle, or your blood. For decades gloves were not worn during these procedures. If you are testing a large number of people, the simple answer may be there was simply a glove shortage.
I agree with the first post. TB tests don't cause much-- in any-- blood contact even with a nurse's gloves. However, I do think you should report the failure to use fresh gloves on each person to their manager or supervisor, because that's probably a violation of their policy.