I am in favor of exposing all of tk where it makes sense to do so, and I think it does here.

After 'translating' the tk after_info entry into tkinter-ese, I would expect and want that
  root.after_info(root.after(f, 100000))[0] is f
be true.  the same as would be true of the tcl equivalent. (This could even be a test.)  It appears that the current patch instead returns a (python) reference to the tcl wrapper of f.  The fact that python callbacks get wrapped as tcl callbacks is currently transparent to tkinter users and should remain so.

Serhiy, I presume that this is what you were uncertain about.  I am presuming above that f can be recovered.

Returning the function kind as 'timer' or 'idle' is fine. In other contexts, an enumeration would be a possibility, but this does not seem to fit tkinter.

I presume a bad id results in TclError.  Do other tkinter functions allow TclError to propagate?  My impression is no.  If so, it should be replaced here in a way consistent with other tkinter practice.