No, the ring adaptor will not work with the Cybex Cloud Z car seat, you'll need a different one - the one with Maxi-Cosi/Cybex U-shaped attachment. I believe they stopped issuing those after the Nuna Mix 2, I guess they're trying to boost the sales of the Nuna car seats, so the best solution is actually to get a Nuna car seat - no problems with compatibility they.
Although, the adapter set for the Mixx 1 and 2 series, on the right:
...should still work on the Mixx Next as well, as the click-on mechanism looks the same. however, I cannot promise you that - as officially, the Mixx Next accepts only Nuna car seats. Could be worth trying, though.