Keep in mind our example is a one-on-one. During the actual tournament, there will be three players on either team, so any one player has to try and pay attention to multiple opponents.
One trick teams will use is called "laning", as in shooting down a lane, or passage between bunkers. This is essentially an "area denial" technique- you're not trying to actually hit another player, you're just trying to prevent those other players from using that "lane" to advance up the field.
If your team can advance further up the field, or at least get one of your players further up the field (your "point man") you tend to have the advantage- not the least of which is, in a center flag scenario, you're closer to the goal.
Also, in more general terms, shooting at a player's bunker, or near/around their bunker, restricts their ability to peek out or lean out and shoot. Again, it's basically 'area denial' fire rather than targeted aim-to-hit shooting.
In our first scenario, both girls ran for cover before shooting- Sandy got to her cover first, and had a second or two to shoot at Pirta while she was still running. Pirta hunkered down and started shooting back at Sandy's bunker, not knowing that Sandy was crawling away from it (and towards the flag) while concealed behind another bunker between them.
In our second scenario, as Jake notes, Sandy's a faster runner than Tawny, but Tawny knows the tricks I outlined above. She only has to watch Sandy (and not, as I said, pay attention to at least one or two other players) and so could focus on shooting directly at Sandy, forcing her to run for cover. In the few seconds Tawny will have while Sandy's behind her bunker, she can keep running and/or pick a more advantageous bunker.