In a manner that is limited in perspective or narrow-minded, often associated with being unsophisticated or not cosmopolitan. He thought provincially, unable to see beyond the customs of his small town.
In a way that relates to a province or the provinces, as opposed to the capital or major cities. The festival was celebrated provincially, with traditions unique to the region.
At the level of a provincial government rather than the national or local level. In Canada, education is provincially funded and administered.