Thanks, mrfixit. After I posted my inquiry, I decided to try the technical assistance number to Toro. I was surprised to actually contact someone,who was helpful and courteous. (Kudos to Toro!)
The person who answered had me get in front of the timer/controller and she walked me through all the settings. Your analysis is spot on, as after this past winter, I found that I had to replace the backup battery (frequent power outages here with our less-than-adequate power provider). The programming had erased, so I reset everything. I made the error of programming separate start times for the two zones. Once I turned off the start time for what I thought was zone 2, the system now cycles and shuts off properly.