I have tried this on 2 differernt Brother MFC 9970CDW printers, one of which is brand new. I have tried all the options in the printer dialog both in photoshop and the printer. I can print other photographs in inDesign and other products perefectly on the same printers. However, photos process in photoschop cc have the same problems even if place in indesign and printed from there.
Photoshop sends the document you have to the printer.
Variations in print that differ from what you have in the document means a problem with the printer, or the printer driver.
Any chance you could post one of the photos that's causing this issue?
Are you using 8 bits/channel? Do you have Dithering disabled?
Notwithstanding what Chris has said, it may be that you've introduced posterization into your document by the way you've processed it. Perhaps it's just not as visible on your screen as in print. But without seeing what you are seeing we can't judge.