@wanfai @JavelinJoe
@Kredim pointed this out, but for a more detailed explanation, it's because she's not actually stopping time, per se. In turn-based RPGs, which this draws heavily from, a person's Agility (Quickness here) determines their order in combat. Say you have four people; their Agility scores are 20, 16, 12, and 8. No matter how many times they fought, they would go in that order during combat. Some magic items or magical buffs can raise a person's Agility, letting them go sooner, just as magical debuffs can force an enemy to go later.
That's in a normal situation. Here, Quickness doesn't determine just turn order, but also turn frequency. Mimit, who has maxed Quickness, could have 5-10 turns for every 1 turn that Aki gets. What Mimit's barrier is doing, then, is debuffing Aki's Quickness to 0, effectively removing her from the turn order all together.
However, the angel egg isn't full encapsulated by the barrier, so it's not effected to the same degree, allowing it to buff Aki's Speed (which seems to effect Quickness to a small degree) to the point of effectively canceling out the barrier's debuff. With Aki's broken Speed, that's all she wrote, really.