Can I have some proof that he can cast spells during other people's time stop? I don't doubt that he can move in them, but that he can cast spells is news to me.
Fūzetsu is arguably also no regular time stop, seeing how it stops causality and stuff (the way the page puts it, even causalities besides time). Although as an anime-only peasant, I admittedly don't know the source text on that.
@GoldenScorpions might know, though.
Imagine the world as a puzzle of 1000 white pieces.
When a Fuzetsu spell happens, the area it covers is cut off from the flow of the outside world. Time, space, motion and existence itself are separated, and they are halted inside the Fuzetsu. The Fuzetsu'd area still exists since people trapped inside can die and buildings can be destroyed, but from the perspective of humans outside of the spell, the Fuzetsu'd area never existed.
To the supernatural entities of the verse, the puzzle has 999 white pieces and 1 black piece (the trapped area), but the black piece is still attached to the puzzle, since it still exists.
To humans, they instead perceive the world as a completed 999-piece puzzle. The 1000th black piece doesn't register to them, because to them it doesn't exist. White the Fuzetsu is active, they don't even think about the black piece; the world always had 999 white pieces.
If we assume a Fuzetsu happens around the Eiffel Tower: while the spell is active, the tower still exists, but humans don't register it as "existing". In humans' perspective, it never existed. But when the spell is undone, the Eiffel Tower goes back to "having always existed" and they don't recall the blank time where it had not.
Essentially, a Fuzetsu'd area is similar to if the Power of Existence of that area had been temporarily removed. While active, humans live as if it never existed. When undone, humans live as if it existed as normal. Same deal with people trapped inside the spell.
So yeah, it's a Causality-based time stop + temporary existence erasure/memory manip/mind manip
I hope that's clear.