As Bill said who moves first is determined by the pdt which isn't necessarily the side that is considered "First Side". After the first turn the "First Side" is always the player who moves first each turn. I think the Scenario file sets "First Side" but I haven't verified this.
Who is "First Side" is determined by the scenario designer. In most cases it is the side that is considered the overal attacker but there is no real rule saying this. The designer may consider other things more important to determining this than just who is the attacker. Also the First side may indicate who has the initiative which may not be the side who is considered the attacker but generally is. That is why Lee is usually the "First Side".
Who is First in a turn has certain advantages and disadvantages on key turns like Dawn, Day, Dusk, Night and last turn of game. These advantages or disadvantages may determine which side should go first. Last turn can sometimes be the determining criteria since it is closely tied to victory conditions such as occupying hexes or exiting map. The designer may set the First Side to prevent that side from making a last turn jump at objectives.
So the short answer is: "Yes, the First Side is usually the attacker, but..."