OG Azem (*SPOILERS*)

[Rulakir]

Emet is incredibly sentimental. I took it to mean he traveled because that's what Azem would have done and he was doing so in honor of them.

As for the quote, I was confused by that as well because Hydaelyn says, "These were the words of the crystal's original bearer." However, Emet created the Azem crystal, so that implies the quote was his even though the scene makes it seem like it was Venat. Edit: Or I suppose unsundered Azem, but that still doesn't make sense given no one 'bore' the Azem crystal before the WoL other than Emet.