This is actually quite tricky if you don't know what you're doing. The call doesn't need answered, so ignore it. Time the hang up as seen and you'll be fine. If you hang up too early, the call will come in while outside the the cab and it will almost always screw you out of getting back in before it pulls off.

The only time you'd ever use a faster vehicle during this mission is if there's something directly behind your cab after the trip skip. If you were to do this, never get too far ahead of the heli or it will slow down. The video shows exactly how to pace yourself if in a fast vehicle. If you're in a cab (99% of the time), there's no need to worry about outrunning the heli. Never slow down, unless you're going to wreck, and follow the route.

Timings (cutscene skip to heli touchdown, before stealing): Taxis (van, two cars): no crashes, no tunnel - 1:47 Comet: no crashes, no tunnel - 1:38

You'd come upon the tunnel if you continued going straight instead of crossing over the sidewalk at the end of the freeway. In my timings, I found I lost a couple seconds by using the tunnel, so avoid it.