This is also one of those cases where "Immersion" serves to confuse rather than inform the statement; I'm perfectly capable of being only-IC without being immersed. The latter is a much deeper experience than simply making all decisions from in character POV.
I mostly mean bleed or emotional immersion in the situation and characters. Coming at those decisions from a place of empathy for the characters they are portraying. Being present in the moment. Pretty much what I would expect from another actor I was working a scene with when I did amateur theater. It's also pretty much the only sort of immersion I personally give two figs about on either side of the screen.
It's about being present in the moment, feeling the tension, and playing with curiosity. Not engaging in all the myriad ways to create emotional distance from the situation or the characters. This scene from Fight Club gets at what I'm looking for.