pathfinder 1e – How does Improved Critical feat work with a Soul Knife’s Emulate Weapon Blade Skill?

You can take Improved Critical Mind Blade (or rapier)

From Form Mind Blade,

She can also choose her mind blade for feats requiring a specific weapon choice, such as Weapon Focus and Improved Critical.

And Emulate Melee Weapon,

The soulknife is proficient with her mind blade in this form and it functions in all ways as the chosen weapon.

The emulated melee weapon ‘counts as’ whatever weapon you Emulate and, if you chose them, Feats and other abilities that specify that weapon would work… but it is also still a Mind Blade and benefits from anything that specifically affect Mind Blades.