I have been using Supershuttle to and from LAX for over 5 years, never had any issues. You get a 20 minute window. Be ready at the start of this window, this is the pick up time on your confirmation. You will get picked up at any time in this window, ie you could end up waiting 20 minutes, right to the last pickup of your time window. For this reason I always choose a pickup time for earlier than I need.
LAX has nightmare traffic at all times of the day. It is shaped like a U, with a one way system. Supershuttle drop off at each terminal in order, starting at Terminal 1. You could be up to 30 minutes if you are getting dropped off at the end of the U at Terminal 6 . Again I always allow for this delay and plan my pick up time accordingly. One time the driver dropped us at the arrivals level of the terminals, as the traffic was way too backed up at the departure level.