I agree that Carlson here was talking about 095, but I suspect the impetus for this article came from someone in intelligence community leaking to WSJ something along the line that Chinese subs are getting really quiet.
I think it is unlikely for WSJ to write an article like this with first line as "China is on the verge of becoming a world-class submarine power, with new technology and a bigger, better fleet that is gaining on the U.S. and its allies" unless someone is telling them this and since 095 isn't going to be inducted in a reasonable number until end of this decade, I think they are referring to 093Bs that are joining service now. Unless 093B noise level from initial sea trials and such have reached a certain level, there is just no reason to be talking about it this early.
Reading the character of the article, I somewhat disagree.
I think their idea of China "gaining" is due to two things:
1. China producing more nuclear submarines than the US is
2. Chinese submarines are expected to get quieter -- but guided by Carlson's views
The article doesn't mention 09IIIBs either by name, or indirectly.
If anything I think the overall argument is one of bemoaning the state of US nuclear submarine production compared to the increase we can see of the PLAN, and tossing the PLAN a bone by recognizing that Chinese submarines are getting better. But if we were to identify what Carlson meant by "really quiet" I suspect he would again say "Akula I level" for 09V.