It all depends on the specific pesticide products being used, what active ingredient(s) those products contain and in what concentration, and, assuming you are in the United States, ensuring that the products are being applied according to the federally approved label.
As others have said, pest pressure varies significantly by location. And depending on what pests you are treating for, keeping your home clean is often the number one best thing to prevent problems from happening later.
If you ever have concerns that a pesticide is not being applied by the applicators (such as your landlord or a company they hire) according to the product label, you can contact your state officials to report a misuse incident. The National Pesticide Information Center (NPIC) has information on how to find your state official:
http://npic.orst.edu/reg/state_agencies.html#mapIf your landlord will tell you what specific products are being applied, you can do more research. If you have the EPA registration number or trade name of a pesticide, you can look a copy of the product's full label online using the Pesticide Product and Label System (PPLS), available here:
https://iaspub.epa.gov/apex/pesticides/f?p=PPLS:1As a quick and dirty indicator, one part of the pesticide label you can look for to to get a general sense of a given pesticide product's toxicity to humans is the "signal word." This will appear near the top of the product's label, and will be either CAUTION, WARNING, OR DANGER. "CAUTION" means the pesticide product is slightly toxic if eaten, absorbed through the skin, inhaled, or it causes slight eye or skin irritation. "WARNING" indicates the pesticide product is moderately toxic if eaten, absorbed through the skin, inhaled, or it causes moderate eye or skin irritation. "DANGER" means that the pesticide product is highly toxic by at least one route of exposure. For example, it may be corrosive, causing irreversible damage to the skin or eyes. Alternatively, it may be highly toxic if eaten, absorbed through the skin, or inhaled. If this is the case, then the word “POISON” must also be included on the product label.