Down-time isn't down-time. Anyone who does any kind of mental work will continue thinking about the work even when they're away from their desk.
They will think about it on the way to work. They will think about it during breaks. They will think about it while appearing to wander aimlessly around the building.
They will think about it on the way home. They will think about it while they're at home, they will think about it in the shower, they will think about while eating or doing something else, and they will think about while they're asleep.
It will take them at least two weeks of actual undistracted full-time down-time to stop thinking about it.
But you can also make them stop thinking about it by piling on distractions - hiring sessions, meetings of all kinds, absolutely critical company events that aren't, and so on.
And you can also make them stop thinking about it by giving them too much to do. Most people have enough mental space for one, maybe two, problem tracks. Giving them more - especially with limited context switching time - and you'll make it impossible for them to solve any of them.
You're not running a physical production line. The typing and the code changes are the output of a complex and surprisingly fragile mental process. If you don't understand how the process works, you're wasting a lot of its potential value.
Not only will people be unhappy, but the quality of their work will suck too.