If I apply through a provincial program, do these representative regulations apply?

Yes. These regulations relate to all applications or procedures under the Immigration and Refugee Protection Act (IRPA). When you apply to a provincial/territorial nominee program, for instance, your application is in connection with an application for permanent residence under IRPA. However, each province/territory may also have its own procedures for dealing with representatives. Check with the province/territory to which you applied to find out whether it places any additional restrictions on citizenship or immigration consultants, lawyers and other representatives in the provincial/territorial application process.