I had not heard that before. A quick review of some sources of the templates shows them starting the turn with the steering axle straight ahead (see http://image.slideserve.com/259312/aashto-turning-...).

They need to be straight; our driving handbook recommends keeping wheels straight to avoid getting pushed into oncoming traffic if rear-ended

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I believe you're correct; the templates as drawn have an immediate transition from tangent to radial at the point of curvature. To mimic real life, there should be some distance (time) for the driver to crank the steering wheel, unless vehicle is at a dead stop before turning. These templates are for low speed maneuvers, and the small transition from straight wheels to full turn not shown is probably not significant.