It would be DM before routing ?
It needs to be DM before routing. It's one of the requirements for any unit to rout. You have to be DM in the first instance, then you can rout.
A broken unit (disrupted or not) just sits and ""Wibbles"" if its NOT DM
It gets DMéd the following ways
1/ unit(s) gets attacked which results in it failing, morale check.
2/ unit(s) location is attacked by a sniper whilst broken if not otherwise marked DM.
3/ a Known enemy unit (KEU) moves to a ADJACENT location of a broken unit(s) if not otherwise marked during the movement phase.
4/ a Known enemy unit (KEU) advances to a ADJACENT location of a broken unit(s) if not otherwise marked during the advance phase.
5/ at the commencement of the rout phase a broken unit that is not otherwise marked which is in open ground AND normal range to a potential fire attack from a KEU.
Hope this answers your question