I don't think it's necessarily that there are multiple TVAs existing simultaneously, akin to multiple timelines (strap in, I'm going to do time travel mechanics; shit's going to get stupid). The TVA and Kang's hideout exist outside linear time, making the causality of Kang creating the TVA all fucky; Kang didn't really create the TVA in the past, because 'the past' doesn't exist in whatever pocket dimension the TVA exists, just an eternal 'now'. Instead, it might be more correct to say that Kang is eternally in the process of creating the TVA, while the TVA in eternally in the process of being created. Killing Kang disrupts that, and now the TVA has now never existed. However, killing Morally Dubious Kang allowed a different, Overtly Evil Kang to come out on top of their conflict and takes his place; he in turn creates the TVA again (just one that fulfills his particular goals). But since, again, causality is all fucky in this scenario, new Kang and the new TVA have now existed eternally in their current incarnations; Loki is now sitting in the only TVA that has ever existed.
In other words, rather than a branching timeline in which all possibilities exist in one branch or another, this is a case of the singular point that is the TVA being deleted and replaced with another one.
Yay, time travel mechanics.