No, players are not being seamlessly teleported to somewhere else like in Portal. Zalarek cavern is indeed right where it appears to be. The only difference is that when you are inside Zalarek Caverns, most of the Dragon Isles stuff (trees, buildings, rocks, etc) above is not being rendered by your computer. WoW already does this with the Caverns of Time in Kalimdor. On the 10.1 PTR, while inside Zalarek, you can use a shaman's Farsight to see Zalarek's ceiling clipping through the surface terrain of the Ohn'ahran Plains (
https://i.imgur.com/OtTseO3.png). You normally wouldn't see this while flying outside over the Dragon Isles, because Zalarek would be turned off. Blizzard can separate where the player icons show up on the minimap (Zalarek Caverns minimap appearing divorced from the rest of the Dragon Isles) from the actual ingame space that the player inhabits (Zalarek is directly underneath the Dragon Isles).
Video of the Dragon Isles surface being turned on/off as you cross a certain threshold in the cave:
https://www.youtube.com/watch?v=maZ27e147EI