X0 is not the midpoints of three windings. It is a common connection of one end of each of three windings, also known as a wye configuration of the windings.I'm guessing that somewhere in the annuls of transformer wiring there's a note that says midpoints of three windings are an XO and midpoints of a single winding are X4.
X4 is used for three phase transformers to denote it is a midwinding tap of one of the three windings which are delta configured. Yet a single phase transformer with a midpoint winding tap terminal is not marked X4. Also, if you have a two-winding secondary, single phase transformer, the terminals are typically denoted as X1, X2, X3, and X4... so X4 does not exclusively denote a midwinding tap.