How does permanent establishments (PE) in Asia interact with double tax agreements?

If a resident of Country A operates business in Country B, between which there is a double tax agreement, the profit derived will not be subject to tax in Country B, unless the business is operated in Country B through a permanent establishment.

If the said business is operated in Country B through a permanent establishment, then the business will be subject to all relevant taxes of Country B, and any qualifying staff will be subject to individual income tax thereof also.