Today there are appx 3,300 Ukrainian with Muzyczuk = Музичук surname residing in Ukraine. Most can be found in what was formerly the Old Vohlynskaya gubernia > Czarist Russia, then divided into smaller regions during Interwar Period under Reconstituted Poland's domain and again during Soviet domain. Others are spread throughout Ukraine, East and West.
The original poster in this subforum has Immigrant Family from Cherkassy oblast, which at one time was part of the old Kyevskaya gubernia, Czarist Russia.
The family in the link you provided were from what is the Kovel raion/district of what is today Vohlynska oblast/region.
You should be able to find your family members here. Start w/the ones still living in Punnichy, which is where the family first settled upon immigration.http://www.locatefamily.com/M/Munyandinda_to_Muntz/Muzechea_...