Yes, Cyper WP is perfectly safe to apply around pets and/or children. When you are applying the product you should do exactly as you suggest, which is keep the pets inside or if applying inside in another room until the product dries. After it dries which is usually about 30 minutes, it is perfectly safe to allow pets entry back into the yard or living space.
Are you having a problem with these pests indoors? Are you just starting preventative measures to make sure they do not become an indoor problem? Cyper WP would be the most versatile and most effective product for roaches and scorpions. Cyper WP can be used outdoors to help get rid of these pests before they make their way in and Cyper WP can be used indoors to help get rid of current infestations. If you have a roach infestation indoors you should also use a roach bait gel such as Advion Roach Bait Gel around counters, sinks, cabinets and drawers and you should add an IGR such Gentrol to the same gallon of water as you mixed the Cyper WP (IGR should be used indoors only.)
For outdoor rodent control you can use the tamper resistant Protecta Rat Bait stations with Contrac Blox . The stations should be placed around the perimeter of your home near areas where rodents can gain entry such as doors, vents, and utility lines that enter the structure. We do not recommend baiting indoors. If you have a current infestation you should use appropriate sized snap traps or glue boards.
It is important to not just rely on pesticides to do the entire job for you but instead to make changes to the immediate environment around your home to help control these pests. This includes moving trash cans to new locations, turning mulch, sealing holes or gaps that allow pests to gain entry into your home and so on. Please read our article titled Integrated Pest Management to learn more.