When accepting a baby sitting gig for the first time you might feel at a loss for what to do. There is no immediate instruction, but don't worry! Just go ahead and accept another job and a phone message from the property you're baby sitting will appear eventually and should provide a menu of actions to chose from at this point. For me it has happened immediately after accepting another gig, and also a few minutes after I'd started working on another job.

Some baby sitting jobs have multiple issues to fix, but so far for me they have been small jobs themselves e.g. roaches or fuse fixing. Some have the option to "send your uncle", during which the gameplay will switch to the baby sitting location and you play as the uncle in the relevant mini-game (e.g. spraying roaches, setting rat traps). Others seem to offer only the options to "send a professional" at cost to yourself, or do nothing.

Another element to note is that these notifications are time sensitive! So keep an eye out for them while working on other jobs, you likely will have to switch locations to catch it on time. missing the notification will trigger a follow up message from the tenant, a somewhat passive aggressive one that removes the options to intervene and solve their problem. This has a negative impact on the overall score and review from the baby sitting gig.

Feel free to provide more information if you have any.

I personally only noticed this after moving out of "The Slums" and into "The Suburbs", but on most babysitting jobs in "The Suburbs" seem to have a bug where they don't complete until the lot is visited. If it's been a while, check the lot. I would usually see something visual "wrong" with the apartment: bugs, a blown fuse. Wait a while and the person will notice the problem and message you, allowing you to address it and induce the final assessment, ending the job.