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The quantum stuff refers to the theoretical possibility of quantum computers to crack asymetric ciphers like the RSA.
There are new, quantum safe algorithms coming right now, but it's hot out of the owen so personally I'd wait a bit for the first bugfuxes and such.
Sure, researching these algorithms is a valid concern. Just advertising is misleading. Since there are no quantum computers around which would be big and reliable enough to do these calculations. And as far as I know we're not even sure if we can buld them at all, or in what timeframe. So they're advertising to protect against something that doesn't exist. I think that should be factored in when comparing services.
And by the way: I think it's mainly the key exchange that is affected. I guess the tunnels are protected with symmetric cryptography? And quantum isn't really an issue for most symmetric cryptography algorithms.
Exactly.
And yes, the handshake is made over an assymetric cipher, and then you use a symmetric one because they (this is not true for all symmetric algorithms out there, but the ones used in ssh etc. are) are both way faster and actually safe against quantum algorithms.