Embarrassing for Jones, and even more so for the lawyer!
A similar incident happened when I was a summer intern for a big firm back in college. We were litigating a case involving allocation of liability for the fatal crash of a helicopter that was supposed to be sent to the White House fleet (it crashed during testing). During discovery, opposing counsel sent our firm a number of boxes that were marked privileged attorney-client work product. The partner in charge of the case on our side ordered the boxes segregated from the rest of the evidence and asked opposing counsel if they wanted those boxes back because they may have been sent over by mistake. The opposing firm replied that they hadn't made any mistakes, and we should keep the boxes.
When the files were opened, it turned out they contained highly incriminating evidence! When our firm tried to introduce these documents into evidence, opposing counsel belatedly asserted attorney-client privilege and demanded they be excluded. Predictably, the judge ruled the privilege had been waived. Same thing, presumably, will happen to Alex Jones.
Do not assume from the moment that you form an attorney/client relationship going forward, that letters, emails, texts, voicemails, anything that is written/transmitted/recorded, will not become discoverable. Even if it is inadmissible under the rules of evidence, once the other side knows your secrets, your case is in jeopardy.
If you truly want to have an attorney/client protected discussion, it should happen face-to-face in your lawyer’s office, with no one else present. That’s called operational security, which is the practical side of the abstract legal protections like invoking privileges after the fact, and hoping that a judge will decide the law of privilege applies in your circumstances.
If the face-to-face communication with a lawyer in the lawyer’s office can be invaded, then civilization has already fallen.