The difference is not large, but there are cases where one sounds more natural than the other.
XにつれてY does not strongly assume cause-effect relationships. It can be used when X and Y change almost independently over time.
Xに従ってY is more explicit on the cause-effect relationship, and thus preferred in technical contexts.
XにつれてY is usually used with temporal changes. (Time is irreversible, so maybe this is what 一方向の変化 in your textbook is referring to?) On the other hand,
Xに従ってY has a wider range of usage.
As night approached, the rain became heavier and heavier.
In this sentence, つれて is more natural because there is usually no direct cause-effect relationship between nightfall and rainfall. But if there is an approaching typhoon mentioned in the context, 夜が近づくに従って would sound fine, too.
Statistics show that the younger one starts learning English, the more accurate his/her pronunciation becomes.
In this sentence 従って is more natural because this is an academic-sounding sentence and "starting age" itself is not something that changes over time.
In this sentence ～につれて and ～にしたがって are mostly interchangeable, but したがって sounds like the speaker is aware of the fact that boys tend to become more silent as they grow up.