How does Siphon Soul/Blood Boil work in regards crit rolls/RR checks? Is it like a normal DoT and checks for RR application/crit rolls on initial application or do they check per tick?
Per tick. There’s nothing different there from any other DoT debuff in the game.
Actual DoT damage effects (Burn, Bleed, Frostburn, etc.) check for crits and resists once per application and then deal either normal or critical damage until that DoT’s duration runs out.
Everything else checks each time it does damage.
So for Siphon Souls the base skill checks each tick, but the Vitality Decay and Bleed DoT from Blood Boil check on being applied each tick… but could continue to do critical/resisted/reduced resists damage (overriding later Blood Boil applications) if you had enough increased Bleed/Vitality Decay duration.