Translation:When will the musicians start the concert?
Is it just me, or is the speaker putting the accents on the wrong syllables: muzíkistój, rather than muzikístoj.
No, komenci is a transitive verb. Hence, komencigi would be redundant in this case.
EDIT: Although komencigi is a valid word, it doesn't have any fixed meaning according to ReVo. Just a note, because some words, like havi (to have), which is transitive, also has the word havigi (to provide), which is also transitive.