Is the social security in Jiangsu Province co-ordinated?

That's right. It may be that one local city is set as an overall planning area, or two or more cities are set as the same overall planning area, and they can only move flexibly within the same overall planning area, otherwise it is called off-site transfer.

Further reading: How to buy insurance, which is good, and teach you how to avoid these "pits" of insurance.