Not exactly. There are 3 scenarios that come to mind.
1. You're driving along on your own, FCW thinks that you're approaching the car in front of you too fast, and it beeps at you. No braking happens. This is good.
2. You're driving along using AP, FCW thinks that you're approaching the car in front of you too fast for AP, so it beeps at you and AP starts to brake. This is stupid, but I've read of it happening (and may have had it happen? can't remember).
Just like if you're using AP, the car shouldn't really warn you that drifted out of lane (well technically you shouldn't be drifting out of lane on AP, but it does happen).
3. AEB activates and it brakes. This is good (assuming there's a car)
So it sounds like you had 1 instance of AEB, and 1 instance of AP doing something stupid and hitting the brakes hard while activating FCW.
<--- armchair engineer