It does not matter the type of contract. All projects need to have a way to process changes because changes are a near certainty for every project in existence and will always be. The process does not have to be complex for smaller, less complex projects but there needs to be a way to understand the change, estimate cost and schedule impacts, estimate risks, and process the change.
Compatibility with original requirements is a non sequitar. It does not matter. If they are incompatible, then the change, if accepted, will change the requirements accordingly.
There should be no question as to whether the customer pays for a change, especially for a FFP contract, but really for all types of contracts. Customers must pay for changes on a project as it alters the original understanding, upon which the cost and schedule was based.
At the beginning of the contract, your estimate for the management of contract should include processing changes. You have no idea how many changes would be requested so there is risk to your FFP if you estimate too low. Experience with doing the work and with that customer should inform you the degree of effort you need to put into your FFP price; however, absent that, you simply have some risk here.