First, you must clean the seats thoroughly. The spots "rings" come from dirt embedded in the fabric that surround the spot you just cleaned.
Once you clean the seats, use a plush cotton towel and press it into the fabric over and over again in an attempt to soak up as much as the dirty solution as possible. Then....the key is to use bottled water to rinse the fabric. Don't use tap water which is full of minerals and other stuff that will be left behind when it dries. Then.....get a second plush towel and soak up as much of the rinse water as possible.
If these "rings" persist, the seats are still dirty. You will eventually get them to go away if you repeat the above.
Good luck!