Not only is it safe to be home while a self-cleaning oven operates, it is dangerous to leave the house while the cleaning cycle commences. Self-cleaning ovens operate at extremely high temperatures and you should stay nearby to handle any problems.
Properly functioning self-cleaning ovens have a lock that prevents anyone from opening the door during the cleaning cycle. Confirm that this lock is functional before starting the cleaning cycle. While you do not need to remain in the same room as the oven, it is helpful to stay nearby to respond to any emergencies, such as an oven fire (turn off the gas or electricity supply immediately and call the fire department).
Some owners may think they should leave the home during a cleaning cycle because of the odors that can result. Most self-cleaning oven produce foul odors due to the high heat and the burning of oven debris. No safety reason requires you to leave the home because of these smells. Open your windows and ventilate your kitchen as much as possible during the cycle instead. Minimize potential odors by mopping up spills before starting the self-clean cycle.
Self-cleaning oven cycles can be inconvenient because they take several hours on average. Schedule the cleaning for a time when you'll be around the home, but the cleaning cycle will not inconvenience you. For example, set the oven to clean immediately in the morning or right after dinner ends. This allows you to stay nearby without needing the oven for cooking.