I asked the designer the question. Here is the complete explanation of the King in the North's Abilities:
Robb Stark-King in the North
Can remove Engagement Token against Fearsome opponent.
His Commit Ability only allows him to change places with an adjacent friendly Cavalry banner bearer figure if at least one figure in Robb's Unit would be removed. Otherwise, according to the designer, this would break the rule that Commanders cannot take hits to trigger Abilities.
This means that Robb Stark's figure alone in his Unit may not utilize his Commit Ability. However, if Robb Stark has at least one figure in his Unit who will take damage (i.e. be removed from play), then he may switch places with any friendly adjacent Cavalry banner bearer, even one that is a different rank (Color) or another Cavalry Commander, or even a different type of Cavalry, and the new figure will determine hits for the original attack. This means that, if the attacker has rolled two red shields as hits and Robb changes places with a blue banner bearer, then those hits will no longer count.
Also, if Robb switches places with a banner bearer that is a Commander, then the new Commander of Robb's former Unit may use Abilities, such as Smalljon's Pursue 1 when counterattacking, in response to the current attack as if the attack had been rolled against the new banner bearer.
While a new Cavalry Commander would simply add Abilities to Robb's former Unit, as usual, Robb Stark-King in the North may switch places with banner bearers from different types of non-Commander friendly Cavalry Units. In that case, Abilities are determined by majority type, with the banner bearer figure breaking ties. So, if Robb switched with a Last Hearth Lancer and there was only one Winterfell Rider left in Robb's old Unit, then the whole Unit (consisting of a Winterfell Rider and a Last Hearth Lancer banner bearer) would behave as Last Hearth Lancers with the Abilities Wedge and Line Formations and Pursue 1.