The AIM seems to suggest that there is no protection beyond the standard airway width. That is not true. Below 10,000 ft, at a VOR you aren't afforded much extra, if any, but above that to 18,000 feet, you are protected in a curve 8 NM beyond the VOR (10 NM secondary protection) and above 18,000 ft the primary area is extended 13 nm past the VOR and 15 NM for the secondary area.
Now, assuming a 90 degree turn in an airway (anyone know of an airway with a 90 degree turn?) how close do you get? Your ground track is a function of your groundspeed, and roughly speaking, a 90 degree turn at standard rate takes 100'th of your ground speed in nautical miles, i.e. a 150 tooling along at 100 knots with a 50 knot tail wind will take 1.5 nm to turn 90 degrees. That makes 2.5 more miles before you approach the edge of the primary area. Remember, this is a turn of 90 degrees. More likely, the turns you encounter are going to be 45 degrees or less, which keeps you much closer to the centerline. SO, if you're smoking along at 9000 ft in a King air at 240 knots toward a 90 degree turn at a VOR, you might want to start your turn early. If you're bopping along in a 172 toward a 20 degree bend in an airway, you have quite a bit of room to complete the turn. That is not to say that you shouldn't turn promptly as soon as you identify station passage, but that worrying about leading the turn is unnecessary.