"Supervised time" refers to a specific period or duration during which someone, typically an authority figure or responsible adult, is actively overseeing and watching over another person. Full definition
The bird should spend large amounts of supervised time outside of its cage, so the cage needs to be of comfortable size when the bird is in it. (rescuethebirds.org)
Giving your baby opportunities to spend supervised time on his tummy can help prevent the flat spots from developing. (health-and-parenting.com)
We recommend that you keep your dog indoors, unless you're present to supervise his time outside. (nevadahumanesociety.org)