This is how it works: Most adults are permitted to return to work and routine activities, though masks, for now, should continue to be required. Anytime someone tests positive — regardless of symptoms — their close contacts are identified. The person with the positive test result and all of those contacts are then required to move temporarily into a government-run, hygienic, isolated environment — probably in a hotel or similar setting — until they can be ruled out as infectious. This process may involve testing if tests are available, or spending two or three weeks in isolation if the tests are not. For anyone who tests positive, the tracing program would extend to their close contacts, and so on.
In Hong Kong, many people get out of isolation in just a few days, thanks to the availability of tests. Daily tests per capita in America today are higher than in most countries with contact isolation programs, so it is likely that a similar pattern would occur among Americans.
This strategy is highly effective at breaking the chain of transmission, not least because contacts are presumptively isolated. Thus, contact isolation does not depend on mass testing but, rather, reduces the load on the testing infrastructure.