Okay, I went back and read it over again, and yes, you're right that the message in question is stamped to the minute 0213.
Here's what I understand (repeating what's been said before):
Cockpit Effect messages go out as soon as they are received.
A fault message opens a correlation window of one minute. At the end of the minute, those messages are prioritized and transmitted.
Of the 25 ACARS transmissions:
there are a slew of 17 messages, fifteen stamped 0210 and two stamped 0211 that are transmitted practically without interruption (with holes for two others), these were received from 0210:10 to 0212:16
Thirty-five seconds later (2:12:51), there's another sequence of three messages: one cockpit effect (stamped 0212) and two more faults (stamped 0211), ending with the one received at 2:13:14.
The gap observed between the message sent at 2 h 13 min 14 s and the one sent at 2 h 13 min 45 s is due, at least in part, to a temporary interruption in the communication link between the aircraft and the satellite
Transmission number 24 is sent at 2:14:20, refers to an intermitten FMGEC fault as reported by the AFS, and on this hypothesis, would be due to re-engaging the autopilot and causing a violent pitching.
So, on this hypothesis, the aircraft was flying smoothly. After the last cockpit alarm at around 2:12:40 (the NAV ADR disagree), things returned to normal. While the messages are going out to the satellite, at around 2:13:15, or at most forty seconds after the last NAV ADR disagree warning (or, if I'm wrong about how the ACARS WRNs are queued, all of seventy-five seconds), the crew punches in the autopilot and brings about the upset.
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So it boils down to Svarin's question about that AFS message: does it imply that the A/P was on?
AFS may be 'Airbusese' for Autopilot, but generally differences in names imply differences in functions. Could a fault in the FMGEC relate to something like its envelope or airspeed functions? Does having the A/P off and being in Alternate Law 2 shut down the FMGEC?
The awkward wording of the BEA is to say, if there were a "Cockpit effect", it would have been a disconnection of the autopilot. From this I don't think we should be inferring that the A/P was on. It _could_ have been, and it _could_ have happened that way, but the questions on the interpretation suggest that there may not be any data to support it.
Whatever the "right answer" is, there will be data that has no relevance. But I'm not sure we can claim that there were no thunderstorms.