Well, let me be straight up: It would be a good idea for you to actually read the help. You have a completely wrong understanding about how AE works and what it does. Even basic screen work is explained in a help chapter....
Shouldn't it just playback normally?
After Effects is not a video editing program. It does not work like a video editing program. If you want to do what you're talking about, use Premiere Pro. (Premiere Pro also has some very good green screen keying tools in it.)
If you want to use After Effects to do more involved compositing work than you can do in Premiere Pro, you should still edit in Premiere Pro first and then bring your edit into After Effects. This tutorial covers doing that. And this page covers how to key out a green screen in After Effects.
But, since you're new to AE, you should really start here.