After you fertilize your yard, make sure to keep your pets away. You don't want your dogs or cats (or other critters) chewing on fertilized grass and accidentally poisoning themselves. As a rule of thumb, it's best to wait 24 hours or more until you leave your pets unattended in a fertilized area.
For convenience, it may be best to fertilize one area of your yard at a time so you can have 'safe' areas for your pets to enjoy until newly fertilized areas have 'settled'. This allows you to best enjoy your yard and keep your pets safe at all times. You want your pets to always be safe in your yard, and their being safe should always come first.