The most common and most likely answer to this crossword clue is the 6 letter word EDDIED
I've seen this crossword clue in The Times
E
D
D
I
E
D
Buddy explains!

The straight part
We know that "followed revolutionary movement" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case followed revolutionary movement = eddied.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does EDDIED mean?
EDDIED verb- To form an eddy; to move in, or as if in, an eddy; to move in a circle.