Surely the amount of cage damage would be related to the amount of time spent in captivity. Maybe these birds were captured in Japan/Korea, transported down the coast by ship and then released/escaped within a few days of capture.
I agree with Geoff C that the lack of evidence of migratory behaviour has to be a factor here - I think it is a stretch to conclude that Varied Tit is a migratory (or irruptive?) species based on a single occurrence of a bird in Hong Kong and a few in Shanghai. These are a very long way from the normal range, and if this species normally migrated one would expect to have seen previous evidence for this in north-east or eastern China.
To me, there is also the issue of the date - even assuming Varied Tit was a short-distance migrant with HK as the extreme southern limit of it's range, wouldn't it be a late migrant (as with e.g. Bull-headed Shrike) rather than a mid-September migrant (most/all of which are continuing further south)?
