No you don't have to pay extra for any minor revisions or changes. The price you pay to post the contest includes unlimited revisions and changes to the designs submitted in the contest till the time a winner has not been selected.
Designers will work on all the final revisions that you ask for during the handover stage as long as they are in tune with the selected design. But if there are going to be any major changes, then the designer might ask for a reasonable price.
Note that designers aren’t obligated to make many changes to their winning designs, so if you want to ensure your changes will be made, ask for them before you declare the contest’s winner.
Note that designers are very cooperating to make minimal changes to their winning designs.