Dave - you got it! Any time an Army is listed on the card it attempts to advance. Sometimes the Armies advance twice (or conduct an action on their sequence twice). Remember that the +1 Strength when it occurs is removed at the end of the turn.
Thanks John! I really appreciate the time for an answer from the designer - many thanks. Congratulations on a fantastic game. One of the best solo games I own - which is so immersive that it doesn't feel like you are playing solo. Hats off to you and please keep it up I played yesterday and actually won... Just. But I'm counting it as a technical loss - I was playing sieges wrong I was using the same mechanic for both the royalist and parliamentary. Until I realised that you only get one roll not two as the parliamentary side.