When you do the translation into a Recursion, as far as I understand, you turn yourself into "another person" (same memory, different foci), but for people in the world (even those with Spark and Quickened), you're someone who has "always existed" there.
The question is:
If you leave the Recursion, is your existence on it "erased"? If so, is it "brought back" when you return? If not, how would the absence be explained? Do you receive memories from your existence in there when you're not there?