No, that's not it. I can't explain it well, but that's just how it is.
The nearest hand-wavy explanation I can offer (which is likely wrong anyway because it's full of nonsense) is that the Six Samurai are being destroyed, THEN the Six Samurai panic and try to kill each other off, but they can't, THEN Spirit saves the equipped monster. That's a nonsense explanation because it implies these simultaneous effects happen at different times, but it's just what happens.
Like, there's two stages to the destruction, when Six Samurai are involved. The first stage is trying to destroy whichever cards are being destroyed (all of them, in this case). In the middle you try to kill off other Six Samurai instead (in this case you can't). The second state is destroying the new targets (in this case, this second stage doesn't actually exist, because you didn't redirect any destruction). Then they're actually destroyed. It's at this last point, when they're actually destroyed, when Spirit of the Six Samurai kicks in. Again, this is nonsense, but I can't explain it. Sorry.