How much time you spend in the house when a new aide starts depends on many factors. The first consideration is how your loved one handles himself or herself in
social situations. Is he or she willing and able to speak up, give directions, and say, "I like this; I don't like that"? If not, you'll need to do that on your loved one's behalf.
It also depends on how particular he or she is about how things are done. I've met older adults who want their dusting done a certain way, while others say, "Don't touch my stuff" and get upset if anyone cleans. If there are a lot of instructions that the older adult wants to give the aide, you should remain long enough to oversee that.
You'll also want to stay to discuss ground rules, especially if there are any that are unusual. For example, most aides follow a basic rule: Don't eat the client's food. But I've had clients who won't eat unless someone's eating with them. So if you want the aide to eat with the person you're caring for, that may take some discussion.
A good approach is to let the agency or the aide know in advance that you plan to stay around for an hour or so to get things established. If you're working with a social worker or geriatric care manager, I often suggest having that person do the initial monitoring, because he or she can be more objective. If you're an adult child hiring a caregiver for a parent, for example, there can be a lot of history, and one wrong word can lead to all sorts of upset. A geriatric care manager can ask the older adult, "How do you want this done?" making the older adult feel respected and better able to direct the aide.