Assasin Ascendancy offers great synergy with Poisons - it will be yet another source of DPS in this build.
With Bladefall your main objective is to cast as many blades as possible - that's why the usual Supporting gems for it are Unleash and Spell Cascade. Both of these Spells are dealing Physical Damage, but the main source of damage will come from Blade Blast, Bladefall is used just so there can be blades to be blasted.
Bladefall skill combined with Blade Blast is a popular choice for Assassins.