If you just pushed "[" that doesn't trim your layers, it moves the head of the layer to that point. So if you did that, then moved everything to 0, everything should still be the same(If all the layers started at 0 to begin with).
For example, just to make sure I understand your work flow and what you did---create a new 20 second comp and create 2 solids. Select Solid 1, go to 10 seconds and on the Number keypad press "*" to set a layer marker. Now go to 15 seconds, select Solid 2 and press and on the Number keypad press "*". Now go to 8 seconds, and press "[" Your layers have moved, but have not been trimmed. If you now bring both layers to 0, you everything will be the exact same.
If you want to trim a layers in-point, move the CTI(current time indicator) to where you want to trim it, and press "alt+[", which is what I think you want to do.
I think another approach you could take, is if you just want your comp to start at 15 seconds, is move the CTI to 15 seconds, press "b" to move the Work area tab, then right click in the work area tab and select "Trim Comp to Work Area" Hope that's what you are after, if not, let me know.
Having an understanding of editing/premiere will give you a basic understanding of AE fundamentals(trimming, alpha, keyframes), but if you really want to learn this program, start here:
Getting started with After Effects (CS4, CS5, CS5.5, CS6, & CC), there are some excellent FREE online tutorials that will really teach you the program.
Johnny Cuevas, Editor
Thinkck.com
"I have not failed 700 times. I have succeeded in proving that those 700 ways will not work. When I have eliminated the ways that will not work, I will find the way that will work."
---THOMAS EDISON on inventing the light bulb.