Great question! My bible (Oxford Companion to Music) shows arps starting on the beat, rather than before it. Then goes on to state arps should not destroy the rhythm of the passage. Somewhat of an oxymoron!
An arp. sigh across one stave means play all those notes arpeggiated. Across both staves means start at the lowest and play through to the highest. And a split arp. sign means play both hands (on piano) simultaneously. Not that that helps, just interesting.
I tend to play arps so that the main note - usually the melody note - gets played in time, thus the arp. comes before the beat. But that's just my style. It will most likely depend on the genre and era, and will be left to the jurisdiction of the player to interpret what the composer wanted.
EDIT: Just retrieved my Elaine Gould's 'Behind Bars', out on loan, which states that 'A chord will be spread before the beat unless the playing style suggests otherwise'.