If you whirlpool while you're chilling, you'll disturb the trub cone when you remove your chiller or move it from your chilling chamber (bucket of ice or whatever). You want to get the kettle to a spot from which you can siphon into your primary, then whirlpool LAST. Let it whirlpool for 15 minutes or so, even if it looks still. Leave your spoon in the kettle during the last minute of boiling and while chilling, so you know it's sanitized. Then siphon from the outer edge of the kettle to avoid bumping or disturbing the cone, assuming it formed in the first place (my first one didn't).
On another note, I personally think that there's too much emphasis on the "cool in 15 minutes or your beer will be ruined" philosophy. As long as it's covered you can take as long as you need. I know one guy who boils, kills the flame, and lets his kettle sit overnight. Never had a bad batch AFAIK. But it doesn't hurt to be quick, as long as you're reasonably smart about being clean.