Fear/CBM mechanics question

In a DR-Badstilla-DM 3v3 mirror match, if my Badstilla is the fastest character on the field, and goes first and spreads her CBM, will it prevent my enemy’s faster DR (next fastest toon) from spreading fear with his opening attack? I would have my team on defense so I can not 100% predict whom my Badstilla would target first.

Thanks I’m advance for your replies!