Damaging Ailments Deal x% Faster Mod Prevents Self-Immolation Ignite Reflect

I am playing Ritualist with Beira's Anguish and 100% reduced effect of ignite on you. Without any source of "Damaging ailments deal x% faster" or "Ignites you inflict deal x% faster" I am able to reflect ignites onto myself and activate Beira's. If I then allocate Searing Heat or equip a jewel with the faster ailments mod, my ignites are no longer reflected onto me therefore not activating my Beira's.