The command logs are a summary of the commands that your controller actually receives from LawnCheck. The commands that LawnCheck sends are based on your irrigation programs, as well as any manually issued quick cycles. It's generally easier to look at your program schedule and start time to understand which zones ran, however you can interpret the irrigation command in your log as follows:
Example Irrigate command:(S)IRRIGATE-->>xi=14:0:0:0:3:3:0:0:0
The 14 is the delay in minutes. The command was sent at the time indicated at the start of the command line. Add the delay to get the time that the command is scheduled to run. It should match your indicated program start time.
The next numbers in sequence are the zone "on" minutes per zone. The zones run in sequence starting at zone 1.