I believe the clock resets. NCAA rule 2.13.b states that the shot clock operator should "stop the timing device and reset it when team control is again established after the team loses possession of the ball, WHEN A FOUL OCCURS, when a held ball occurs except for 2.13.c.4, when a try for goal strikes the basket ring, or when a violation occurs.
2.13.c.4 states that "during team control as defined in Rule 4.7.b, a defensive player causes a held ball and the possession arrow favors the offensive team.
You didn't have that here. The double foul caused you to go to the arrow not a defensive player causing a held ball.
Therefore, in this situation, you go to the arrow but the shot clock is fully reset regardless of whether the offensive team got the ball according to the AP or not.
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