Take another look at the original sentence:

Fred blew and blew on the globs of liquid white-out, but they refused to dry when the professor called time, Fred closed the cover of his exam book and hoped the pages wouldn't cement together.

You chose to fix it the correct way:

Fred blew and blew on the globs of liquid white-out, but they refused to dry; when the professor called time, Fred closed the cover of his exam book and hoped the pages wouldn't cement together.

They refused to dry is one complete sentence. When the professor called time, Fred closed the cover ... begins the next complete sentence. You are always correct when you use a semicolon between the two complete sentences that create the comma splice.

Go to the next sentence.

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