Master Yi's double strike isn't getting a proc'd and alpha strike passive

When play master yi when you alpha strike your autos reset the cooldown of alpha strike, when double striking this should reduce it by 2 seconds. However after double strike has been proced once the next double strike doesn't lower the cooldown of alpha strike. Another thing with master yi's passive is that sated devourer is not procing master yi's double strike passive. In the first sequence it should go AA[1/4]-AA(with sated proc)[3/4]-AA(double strike) then the second sequence after the first proc of double strike should have the first hit on double strike already proced leaving 1 hit already on for the next double strike proc, like this AA(with sated proc)[3/4}-AA(with double strike). This does no occur, the sated proc doesn't help the double strike. Based off how the jax proc works on his ult passive it should allow you to proc double strike. This coupled with the fact only your first proc of double strike decreases your cooldown of alpha strike severally impacts master yi.