I'm a little confused with what hand to use where on the bottom of the second page, the part where the arpeggios start.

Currently, most of the arpeggios are being done with my left hand because the stems are pointing down. The only place I use my right hand to "help out" is when it seems simpler to get my right hand to do it.

Am I technically playing it incorrectly? I see many people on youtube playing with the right hand whenever the arpeggios touch into the treble clef, where I usually just continue with my left hand. My teacher suggested that it probably doesn't matter because A) the direction of the stems B) I'm not getting tested on this piece, it's just for fun.

Any ideas?
Thanks

No. There really isn't any way of playing anything correctly per se in terms of which fingering/hand to use. If it works for YOU then that's all that matters.