I’ve read it thrice and I am unsure what it is even they are disclosing in that paper. It is scant on technical details.
In the IETF’s version of Privacy Pass, a single entity being the Attester (payments provider, probably in this case), the Issuer (the mixer service, I imagine), & the Origin (the phone service, I guess) means the main possible way to retain its unlinkability guarantees (Issuer-Client, Origin-Client, and Attester-Origin unlinkability) is for the Client (the user, I take) to be virtually anonymous on their own.
And so, they’ve had to go “double blind” / “double Privacy Pass”… but how it technically has been architected is far from clear. And the fact that they haven’t actually done so probably means the use of “Privacy Pass” here is just a marketing thing (not new), at least for now.