Sylvie kicked Loki back to the TVA before killing He Who Remains Kang and before the timelines started to branch like crazy . . . . but he sat in the "time theater" (empty room) for a while brooding, before going to look for Mobius.
Sylvie killed Kang Who Remains, and the timeline branching went into overdrive, BEFORE Loki found Mobius and B-15.
It was only a few minutes, but it was enough for the reality of the TVA to change.
There are not multiple, simultaneous versions of the TVA, as it exists outside of time and space. The timeline of the TVA itself was altered.
How exactly this happened, well, we'll find out in season 2.