You're always expected to be sensible. :) But it applies to extended contested rolls, too, so long as they are mundane actions. (It does not apply to non-extended contested rolls, naturally.)
So, yes, it would apply to a car chase. You take advantage of quick shifts in lights and traffic; you roll with the changes better. However, since car chases don't take very long to begin with, the savings in minutes and seconds are minimal. It definitely applies to picking a lock.
To the issue of your follow-up question in the comments:
But does that mean I get twice as many rolls as the other contestant? How does time management affect picking locks or what about 'climbing'?
You don't get more rolls than your opponent, if you have one; it's that half the time is taken between each roll, so the whole affair is completed faster. It's for making the extended action take less time, not getting a speed advantage in the contested part.