Which one of these intepretations of belonging of a factor of production is correct in context of calculating "income of our citizens abroad"?
The right (and shorter) name for " income of our citizens/corporations abroad" is "the national FFI", where FFI stands for Foreign Factor Income. I will use this name.

The second interpretation is correct, it will lead to correct calculation of the national FFI. If our corporation/citizen gets income from a factory that they own, but said factory is located abroad, then said income will contribute to size of the national FFI. Also, if instead of the national FFI we will calculate FFI of foreigners, then we will calculate their FFI taking in account what factors they own in our country. For an example, if Ivan from Russia will get income from a factory that they own in the UK (We assume that the UK is our country), then said income will increase FFI of foreigners.

The second interpretation also applies to the land. Just replace a factory with a mine. 

P.S.

Comment by @1muflon1 that made this answer possible 


  @user161005 okay
  but that’s then completely different question then your original. Here
  the answer would be that for GDP you use 1. i.e. the location. For GNP
  2. i.e the ownership. For NFFI both 1 and 2 at the same time. For FFI of home citizens you would use 2. For FFI of foreigners you would use
  also 2 but from their perspective. btw if this is what you ask pls
  edit your question and I will update your answer accordingly. In you
  question you only ask about NFFI which has to use both 1 and 2 at the
  same time since NFFI basically gives you difference between measuring
  with these definitions