The spoiled princess is not Emina's commander. Currently Emina is officially a dead person and a member of the Musou Iron Knights mercenary group (translator's note: musou means unparalleled). She didn't have any particular reason to exit her mecha. She could have just left. It's not her job to keep safe a princess who does very little to keep herself out of harm's way. That would be utterly unreasonable. Her only mission was to get the princess to the camp of an enemy general, for negotiations. It was not her mission to get her out of there if things turn bad.
But then again, Emina has been shown to be as stupid as the author of this story, so it can't be helped.