Some parts of the design/planning/construction process have fixed charges, which you pay direct to the contractor or to the local authority. Other parts involve architect’s time and expertise and are charged for based on how much time is taken.
Before you ever appoint an architect, he will give you a detailed explanation of how (and how much) he charges for your type of project. If something unexpected occurs, and there’s a need to charge you more than first agreed, he will let you know early enough to discuss options – it could be that the project comes to a halt because of objections or weather or environmental factors, or that the client’s ideas take a different direction.
Now and then, a project sails through with far fewer problems than anyone imagined, and Dave charges less than expected!
In any event, the client is always in control of what costs are incurred.