They can do it in their free time, and even barter trade. But from sunup to sundown (or whatever labor scale they use to measure shifts) they are doing something materially useful. No contribution, no food that day. Should only take about 3 weeks to get rid of all the slackers (and I say that as a slacker myself) either they've gone back home, or they've starved to death.

I propose that political officers be sent to these psychics randomly. The officers would sit down with these plebs and ask them to read their futures. If they don't guess that they're going to get beat up, then they're going to get beat up for being frauds. The ones who know what's coming to them, will still get beat up, but lightly, and they will be asked nicely to contribute something more meaningful to society... or else.