These variant subraces are not connected to a specific campaign
Mordenkainen's Tome of Foes is not connected to any specific campaign, and the first few chapters are generic "global" changes (emphasis mine to draw attention to the generic language):
The first five chapters present material for a Dungeon Master to add depth to a campaign that involves the ongoing conflicts described there. Options for players are provided as well, including new character races.
That being said, it is ultimately up to the DM whether tiefling of other lineages use the different statistics of these variants or just use the default tiefling in the Player's Handbook (emphasis mine):
At the DM’s option, you can create a tiefling character who has a special link to one of the Lords of the Nine Hells.
On the Cosmology
In D&D lore, Mordenkainen is from Greyhawk:
...this book contains the musings of the renowned wizard Mordenkainen from the world of Greyhawk. In his travels to other worlds and other planes of existence, he has made many friends, and has risked his life an equal number of times, to amass the knowledge contained herein.
So far, Greyhawk's only official campaign book in 5e is Ghosts of Saltmarsh which makes no explicit mention of tiefling variants. (Greyhawk was the ‘official’ setting of Advanced D&D)
The Nine Hells (along with other planes discussed in the book, like the Feywild and the Astral Plane), are the same locations in reference to any of the many D&D worlds (or crystal spheres according to Spelljammer). This is only the official cosmology based on past editions and designer comments, though.