Insurance companies follow the same protocol whether you do the work yourself or hire somebody. They view the damage, make an estimate, and then cut a check for the actual cash value of the items claimed. They do like to be informed if you are making repairs yourself, however, so you need to look at your situation first. If you already told them you would be repairing the damage, or happen to be a licensed contractor there should not be a problem. If the opposite is true you need to take a look at that specific insurance company. Depending on their policies there may be a slight problem if you failed to inform them that you were making repairs.
Many insurers are pretty lax when it comes to claim payoffs. They only require minimal documentation to prove repairs were actually made. Some do require a certificate or some kind of proof to release any replacement cost value that has been withheld. This is the only negative thing that can happen. They will issue you the ACV no matter what. If you are a contractor you can generate a certificate yourself, otherwise you just need to provide some form of documentation. Once they get it you will receive a check for the remaining funds. Again, this depends on you not informing the insurer you were making repairs.
In your specific case, however, it appears they already paid the RCV value. RCV value covers the replacement of damaged items like appliances. So if you have already received a check for those then the claim has been fully finalized. So just deposit the check like you would any other. If they come around asking question later you will have to address it, but most of the time if they do not say anything you are in the clear.