No, the commission has 14 members. 5 Dems, 5 Reps, 4 Indys.
3 of the 5 Dems, 3 of the 5 Reps, and 3 of 4 Indys have to agree on the final map.
The Chair and Vice Chair rotate from meeting to meeting.
http://www.wedrawthelines.ca.gov/commission.html
The state legislature obviously has a committee as well but is in a clearly diminished role.