Battlemage's cry + Phase run

I have question about this interaction.

Let's say I am using ground slam skill, which hits enemies consecutively.
Then I have battlemages cry linked with phase run.

Does it proc the phase run's more melee phys damage, whn I slam with ground slam exterted battlemage's?

I expect it should, as I perform a slam, it shall give me for 0.2 sec the boost. Even if it is not about performing the skill, it shall proc when it hits first enemy anyway.

Is my conclusion correct or I am just wasting a slot?

Thanks for your answers in advance