Review the original item:
Fred blew and blew on the globs of liquid whiteout, but they refused to
dry when the professor called time, Fred closed
the cover of his exam book and hoped the pages would not cement together.
You chose the correct way to fix the error:
Fred blew and blew on the globs of liquid whiteout, but they refused to
dry;
when the professor called time, Fred closed the cover of his exam
book and hoped the pages would not 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.