Action filter are executed just before the Action on which they are applied to. If you have global Authorization filter, that means they are registered globally and you don't have to decorate each action with those filters, but that does not change behavior of Action filters i.e. to execute just before the action.
Controllers are initialized first and then corresponding Actions are called, so your authorization filter will be executed after Constructor of Controller and just before the action. This is behaviour of Action filters as they are designed so.
If you want to execute authorization before controller construct, try creating Message handler for authorization instead of Action filter by inheriting DelegatingHandler class.