[PeteF]

The reason your center caps are recessed is because the spinner is not fully engaged on the hub. Your new wheels are apparently thicker than the old ones, and I see two exposed threads on your spinners. That may overload the remaining threads on the spinner and become a safety issue. Especially if your spinners are aluminum. I highly recommend you trim the wheel thickness to get full engagement, as others have said. Just trying to keep you safe.