I never actually thought about that, because let's face it, the only way we know we were immerse if it the immersion breaks. I think of immersion in the vein we forget we are in a room holding a controller and we are actually experiencing a character to reach his/her/their objective. I'll put some examples:
The Mario series: Yeah, Mario faces the stereotype that his games are always rehashes from the previous ones with nothing added, but Mario lacks in plot he makes up for gameplay, sure a plumper who jumps 5 times high is unreal, but the way we control is quick and responsive, most if not all of his games, Mario's movement and flow is set to perfection, since he's jumpman and jumping is his main ability. Even NSMB Wii and NSMBU, the two most similar games in the series do feel different if you play them back to back.
Silent Hill 2: This example had to come, because unlike above the controls are bad, yet the game's atmosphere, soundtrack an general sense of dread keep you on your toes, so the controls actually enhance the immersion and would actually break if you could properly fight and defeat the monsters, the fact the controls are bad makes you want to run away, or to avoid altogether, because repetition would kill the immersion too.
And now my two cents in Motion Controls and VR. Motion controls and VR must somehow contribute to the feeling of immersion, and motion controls had their highest points with Nintendo games and their definite low points with Sega games. In games like Mario Galaxy 2 and Metroid Prime Trilogy, you had to use the cursor to point at things on the screen and depending where the sensor is, this could be bad for reaching the feeling, but they succeeded, the pointer was precise and worked.
Now compare that to Sonic and the Secret rings, a game where you use the motion control to make Sonic go left or right, and that is really bad, considering using the arrows would have resulted in a superior experience, this use of motion control was the definiton of 'tacked on', something we would see in a lot of SEGA games for the Wii. I think VR is still needs to fail a little more before people feel like it's uncanny immersion like the Kinect, where you had to move your body to play, but since your body would feel that there's something wrong, you get the feeling that keeps driving you out of the game.