に従って and につれて: following instructions or linked changes
Distinguish acting according to a standard from a change progressing alongside another. Compare shared change contexts with instruction contexts where the expressions cannot be exchanged.
Acting according to a standard or instruction
説明書に従って、部品を組み立てます。 means assembling parts according to the manual. The noun before に従って is a guide for the action, not something gradually changing.
係員の指示に従って並んでください。 asks people to line up according to the staff member's instructions. 指示につれて does not naturally preserve this meaning of following directions.
One change progressing along with another
気温が上がるに従って、雪が解けていきます。 connects the progress of rising temperatures with melting snow. A dictionary-form verb precedes the expression, but this is not limited to a single present or future action.
気温が上がるにつれて、雪が解けていきます。 can also describe naturally linked changes. A past change is possible too, as in この道を進むにつれて、景色が変わりました。, where the scenery changed as the speaker proceeded along the road.
Neither a fixed ratio nor a single trigger
慣れるにつれて、不安が減りました。 means that anxiety decreased as the speaker became accustomed to something. The following verb determines the direction: both changes need not be increases or follow an exact ratio.
For a result immediately following a single action such as pressing a button once, 押すと画面が変わります is suitable. Check for change or progression when using につれて rather than replacing every conditional expression with it.
Quick check: Can につれて replace に従って in 規則に従って申請してください。 while preserving the request to follow rules?
Show the answer and why
No. This requests an application made according to the rules. につれて is used when one development accompanies the progress of another.