ESPN uses the NFL's scoring model for D/ST fantasy scoring. If your offense has a turnover resulting in a score by the opponent's defense, your defense will be negatively impacted.
It's standard procedure that ANY points scored against your selected D/ST team will affect their point total. It's not necessarily how many points were scored against the actual defense of the team. It's how many total points were scored against the team.
EXAMPLE: In the first week of the 2012 season, The Browns' defense intercepted Vick's pass and returned it for a touchdown against the Eagles. These 6 points were counted against the Eagle defense when you look at NFL stats.
D/ST SHOWING POINTS AT GAME START
ESPN awards points to a D/ST for preventing the opposing team from scoring and minimizing offensive yardage.
For example, standard ESPN FFL scoring awards 5 fantasy points for a D/ST that has zero points allowed in that week's game. Further if that D/ST holds their opponent to 100 or less total offensive yards, they will also earn 5 points.
Since ESPN has Live Scoring, at the beginning of every Fantasy matchup both D/STs will have zero points and zero yards allowed. Thus every week your D/ST will start with 10 points on the Fantasy Scoreboard. As with all positions, this score will change as the game progresses.