I remember (watching the show in reruns as a kid) the robot as the B-9 Environmental Control Robot. On his packaging (a box or a metal cabinet, I think) you can see the name G.U.N.T.E.R., which is an acronym for General Utility Non-Theorizing Environmental Robot.
It should be your mantra whenever you apply products to the lawn. This doesn't have to be a lengthy ban. The Dog Owner's Guide suggests keeping pets off treated grass for 24 hours, as nitrogen can burn the pads of a dog's foot. The guide also recommends keeping pets indoors during application to prevent an airborne inhalation or skin contact.
Since each lawn is different, you need to visually determine whether your lawn needs additional fertilizer, but most people can expect to fertilize again within three to four weeks of planting -- or when the grass is 1 to 1 1/2 inches tall. This encourages deep roots and inhibits weed growth.