Perhaps I'm missing something, but why wait for symptoms? Why not test him anyway? Is there any downside to testing? If not, then seems outrageous not to test the PM whose wife has recently tested positive.
The test may be more likely to be a false negative in the early stages of infection. As a result, it may be better to quarantine people who have been exposed without testing them and only test them after they develop symptoms. Otherwise you may be telling someone who has been exposed and is infected that they're not, and then they don't bother to quarantine themselves and go infect other people.
According to Chinese reports, the body part from which you take samples affect the result pretty significantly. There are people who tested negative multiple times from throat swabs but positive from lung fluid or anal swabs.
Not enough tests to go around? So preserve them for who needs them.