His high attack speed with items lets him push towers extremely fast with auto attacks and reduces the Q cooldown.
Former-- "push towers extremely fast"-- is quite false. Yasuo does not build a lot of turret-applicable on-hit damage; as he builds Critical Strike instead...
And the latter is obvious, because his Q cooldown is not affected by cooldown reduction.
Additionally, it is possible to run from a Yasuo-- just don't run towards your own creeps (which, I know, sounds paradoxical). You can dodge his Qs (though to be perfectly honest, this one is close enough to impossible as Yasuo gains AS).
Lastly, sometimes his basic attack damage is rolled into his Steel Tempest casts, like how Vayne's Tumble appears alone even if Vayne's performed basic attacks outside of Tumble.
Lastly, 1.5k from Steel Tempest in <5s is somewhat... irresponsible data. 1) How much armor did you have? 2) How much health did you have? 3) How much Armor Penetration did he have? 4) How much damage did you shield? 5) What items did Yasuo have?
Those are all important; and some of them can't be known at all...