Whether each does so quickly enough to suit Moiraine, however, is another matter, so you may be right about her absence from Ebou Dar. Still, ALL roads lead to Rand now, including Mats; he and Moiraine could as easily go to Ebou Dar together after a reunion with Rand as before one. The biggest problem with that is neither Moiraine nor Rand will want her out of his sight (or vice versa) once they are rejoined, but then, the Seanchan prophecies contend Rand has another rendezvous of his own scheduled with Tuon. Mat going to Ebou Dar is not so surprising; I doubt he wants to leave his blushing bride on her own long knowing the Last Battle is imminent (arguably already begun,) particularly given that intrigue and assassination is to Seanchan what baseball is to the US.