Basically once you (or an ally) or an enemy is in the CAST part of the timeline, an attack against you/them will cancel (interrupt) the action being performed and the timeline timer for that character will be reset.
So, for example, say you and an enemy are close to each other on the timeline but they are slightly ahead of you and begin initiating their action (i.e. enter the CAST area) first. If Igniculus (your daughter, in this case) uses the Glow ability to stun them-- which slows down their progression along the timeline-- long enough for you to get off an attack on them, whatever they were prepping to do will be cancelled/interrupted.
Same goes for you when you are in the CAST phase. That's why it's important to note how long a particular action is supposed to take to completion. If you fire up some big attack that takes a long time to get ready and an enemy enters in the CAST phase while you're still prepping, there's a good chance that they'll attack you and your attack will get interrupted. Does that make sense?