Q:

How was Kaecilius able to break through Doctor Strange's time magic?

Be aware: the whole question is basically a major spoiler!
In the last arc of Doctor Strange (2016), Strange and Mordo

 arrived in an already destroyed Hongkong. Strange then used the magic of his infinity stone to rewind time, presumingly aiming to get to the point, where everything was okay.

But while doing this, Kaecilius managed to break the effect on him.
How was he able to do this?
How did he get to know, that something on a different timeline was affecting him AND breaking the effect?
I mean, Strange used

 an Infinity Stone!

How comes, that some above-average mage was able to break

 the effect of one of the six strongest forces in the universe?

A:

Because Kaecilius understood Time and how to operate outside it
During that battle, Kaecilius and his Zealots had been infused with the power of the Dark Dimension (Dormammu's realm), a dimension without time. While Strange was rewinding, Kaecilius and his Zealots were aware of the change and used their dark power to make themselves effectively "timeless", thus becoming unaffected by the rewind. It's kinda difficult to rewind something that is unaffected by time.
One could argue that Dormammu would have been able to break out of Strange's time loop in the same way, but Dormammu doesn't understand time, because his realm doesn't have any, so he didn't even know he had the power to do that. This is evident from the fact that Dormammu, like Kaecilius, was aware that time was being altered in some way whilst Strange was using the Eye of Agamotto. He just didn't understand how to counteract it.

