Maintenance for the week of April 6:
• [COMPLETE] ESO Store and Account System for maintenance – April 8, 9:00AM EDT (13:00 UTC) - 6:00PM EDT (22:00 UTC)
Swallow Soul counts as a projectile, no matter what it may look like.
And the death recap screens attribute reflected attacks to the other player which accounts for the confusion. You arent the only one to question this, and it would be nice if ZOS updated them to include a (Reflected) note or something like that.