I doubt that the BoS chapter in the Mojave has any communication with the East Coast one. The Mojave chapters is isolated by the Elder's choice. It doesn't have contact with anyone.
The Capital Wasteland chapter says they don't have contact with any other chapter either, IIRC. Specially because Elder Lyons would have been branded a traitor for abandoning the BoS creed and ideology.
So if in FO4 they say there is contact, it was most likely after the change of leadership.
Also TTW should not follow FO4 lore, if it is not in the games. Not even Bethesda follows FO3 and FNV lore in FO4. There is no reason for TTW to do that and change the actual games' lore to accommodate FO4. That would be best as a mod
.