Does flaw in asphalt driveway need to be repaired; and if so, how?
First of all, what you describe sounds like job done improperly. Perhaps you can even use the contractor warranty and have it fixed for free.

Asphalt pieces put from different loads will usually have perfect adhesion to each other - the previously put asphalt is still very clean when the newer asphalt is put, so new one will attach to it perfectly as if it was a single piece with almost no joints. Since you see asphalt peeling off there's likely a problem - most likely the asphalt or the base underneath it got dirty and that prevented good adhesion. No good adhesion - prepare for more peeling off as time progresses, especially since you have temperature variations and freezing water.

IMO it's worth cutting asphalt at the flaw spot deep enough and sealing it with a cold patch to prevent further destruction. If destruction progresses along the joint the same should be done along the whole joint.