I think this highlights an advantage of following the chord tones rather than scale tones. If you're basing your improvisation on a scale, then as you said, when the key changes you'll have to hear it coming, so you can switch to the new scale at the right time.
On the other hand, if you're basing your improvisation on chord tones then the new key won't be a problem, as the chord tones of each chord will be right for whatever key is in place at any time.
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