WoWDB

The vendors for each event only show up on that week's respective event 

Cupri is located in Shattrah City in Outland and only available during Burning Crusade Timewalking Event. 

Auzin is located in Dalaran and only available during Wrath of the Lich King Timewalking Event. 

Kiatke is located in Orgrimar and Stormwind and only available during Cataclysm Timewalking Event.

Each vendor has exclusive gear so if you were, for instance, trying to find Cupri during the Cataclysm Timewalking Event to buy an Azure-Shield of Coldarra you will find she is not there and you will have to wait until the Burning Crusade Timewalking event. That wait combined with the item level of the gear (675) makes Tanaan Jungle Apexis dailies a much more viable option for gearing up.