How is Bayek hearing about the coronal mass ejection of 2012?

This message was intended for Layla, not Bayek. But it was known that Layla would be activating that stone while reliving Bayek's memories. Pay attention to the message itself.

The language of time works in many ways. Two of which you can understand... as you are now.

Layla is "now" reliving Bayek, so her mind is engaged in two timelines: her own and Bayek's. That is what the above quote is alluding to.

The fact that this is part of the message proves that the message was written with the knowledge of Layla's existence, and therefore modern day knowledge, such as what Desmond would've been doing 5 years before Layla relives Bayek's memories.

Can anyone explain how the recording of an event that takes place in 2012 is being viewed by Bayek in 49 BCE?

Bayek isn't viewing anything that you know of. Bayek's simulation (as experience by Layla) is viewing that message. Keep in mind that what we see Bayek do, as far as the story is concerned, is a simulation of the past, being replayed at the present time (Layla, 2017).

The Animus is not like a movie, whereby you see the actual past being replayed exactly as it happened. It's more like (funnily enough) a video game, where the player (Layla) has free range of movement within the simulation to approach things as they see fit, and the simulation will do its best to remain historically accurate.

There have been a few instances of modern day protagonists conversing with their historical ancestor (and I don't mean like in AC Odyssey - I'll not elaborate because of spoilers), but I mean instances such as Ezio knowing about Desmond.

As the lore has never incorporated true time travel, only an exceptional knowledge of things to come (part of the Isu mystique), the most likely explanation is that the simulated ancestors are at least to some degree sentient simulations (supported by the fact the Desmond and Subject 16 are able to be locked in the Animus while remaining sentient), and thus Desmond talking to Ezio is something that did not happen in the actual past, it's just the Animus being less-than-perfectly historically accurate with its "Ezio AI".

Similarly, that message to Bayek/Layla would then have been "hacked" into the system, in the sense that it isn't part of the actual simulation, but the Animus software was changed to forcibly inject that non-historical snippet into its simulation, like how I could put a random picture in this answer that doesn't need to be on topic.