This phrase isn't about animals. It metaphorically compares unsupervised people to 'mice' who misbehave. The interns started playing games as soon as their supervisor left — when the cat’s away, the mice will play.
Pro Tip 2/3
Unsupervised Freedom
The 'cat' represents an authority figure. Without them, people feel free to do as they please. They started a prank war while their manager was away — truly, when the cat’s away, the mice will play.
Pro Tip 3/3
Not Just Rule Breaking
The phrase can also imply indulging in activities that aren't usually allowed but aren't necessarily bad. The team ordered pizza for lunch when the health-conscious boss was away — when the cat’s away, the mice will play.