[Edi]

It's a feature.

Just take a look at the shortlist to see all the siege related issues. This is one of them. Sites in a province belong to the one who controls the province. In a siege situation, neither side is in full control of the province. The one inside the castle controls temple, lab and magic sites. The one outside controls the tax rate (but does not get the income) and PD (if he gets some by event, for example, but he can't buy any).

Because control is split this way, the province shows up in the nation overview, in which case it also shows the sites.