In Return to Bandar Eban, we are told that "Rand had sent his father-along with one of the Asha'man-to the Two Rivers to prepare and gather them for the Last Battle." This might explain why Perrin says in Gateways that "Tam's been gathering what extras he can from the Two Rivers." Of course, I'm not entirely sure how Tam knew where to send them.

I missed that.

Rand probably used the colours to determine Perrin's location (was it already Caemlyn?) and must have told Tam before he left.

If Perrin wasn't in Caemlyn then, it's a mistake Brandon made, or a confusion (eg: Rand told Tam to gather the men in Caemlyn, without knowing Perrin was heading there.. and Tam met Perrin there, before he moved north for the gathering.

We'll probably never know for sure... I doubt AMOL will return much, if at all, to this timeline - unless there's a short prologue with scenes set before the big gathering (that I expect will happen in an early chapter... probably not the first, as I think it would make more sense to give the main characters an intro scene on their way there first.