[DiapDealer]

I'm not following at all.

When splitting a file that has title tags, the result (with Sigil 0.9.1) will be two files with the exact same title tags (blank or otherwise). Sigil neither removes nor adds nor changes their contents.

If your file has no title tags to begin with, then that's invalid. You need to add them. Sigil is no longer the invasive "Fixer of all invalid code." Its clean-source settings are mainly concerned with code being well-formed.