Thanks for the tutorial....I LOVE that move!!! It's so much fun! However, (and not to rain on your parade) it's NOT what I would call a split-time butterfly weave...it is much more. The butterfly weave is called this because the hand motions are similar to weaves while retaining opposite direction spins (butterfly). For example, a 3 beat butterfly weave has the exact same hand motions as a 3 beat weave...only with butterfly directions of spin. In this move, one hand always stays on top. Unfortunately, it has no REAL name that I've ever seen. I call it a 'split-time butterfly 180' in this video (which is somewhere on the site as well).
The names aren't a huge deal, really but I just wanted to distinguish between this and the 2, 3 and 4 beat split-time butterfly weaves which are quite a bit different.
On a further note (after experimenting with my poi), I would say that if you just did one side of this (from the front to the side and then back....alternating) it would be a split-time 2 beat butterfly weave, but when you toss it back to the other side (without a spin in the middle...which kinda resembles a pirouette, but only half of it) it becomes something else. Like I said, I don't really have a good name for it, but I think something with 180 in it would be appropriate. Who knows....but I'm glad you posted the vid cause it will likely help someone learn the move (which is WAY more important than the names EVER will be).