[M T]

The problem with the above analysis is timing. The SCC number of positives who were contacts to a case includes all contacts who tested positive at any time. They may have been tested initially and been negative, and then a week/a day later felt ill and got tested. The idea that testing people who are known to have been exposed should result in more positives is reasonable. However, it may be that if you test "immediately", they aren't sick yet. Unless you have THAT number, you don't know how effective immediate testing is. It may be that almost nobody who is asymptomatic tests positive when tested "immediately". Perhaps it is better to wait a few days. I don't know the answer, but unfortunately the "contacts to a case" number doesn't tell us.

No, if I were exposed to COVID on April 1 and tested positive on May 30, then the contact would not have been reported.

If the average time to symptoms is 5 days, and a person is infectious 2 days ahead, I'm pretty sure the PCR-RT tests would pick up such an average person around 3 days after exposure. 

A relative who had an exposure on a specific day (and was quarantined by the next day) was told her county wouldn't test her for 5 days after exposure (remember, in quarantine, you can't go get yourself tested; they have to come to you), and in fact didn't test her for 11 days.  Her 14-day quarantine expired before she knew if she was positive (asymptomatic) or negative.
IMO, she should have been tested at 5 days and at 14 days after exposure (if the first was negative and no symptoms have developed).

More testing (say at 8 & 11 days) can give you a better idea of when the disease starts (if asymptomatic) so you can wait out your 10 days in isolation once you get a positive test.  If you test at 14 days and get a (first) positive, you will need to isolate until 24 days after exposure.  That's a long time when maybe you would have tested positive at day 6.

If she tested negative at 5 days and positive at 14 days, she should be counted as one that got it from a contact.  (Remember, she was in quarantine so she wasn't further exposed.)

[M T]

The problem with the above analysis is timing. The SCC number of positives who were contacts to a case includes all contacts who tested positive at any time. They may have been tested initially and been negative, and then a week/a day later felt ill and got tested. The idea that testing people who are known to have been exposed should result in more positives is reasonable. However, it may be that if you test "immediately", they aren't sick yet. Unless you have THAT number, you don't know how effective immediate testing is. It may be that almost nobody who is asymptomatic tests positive when tested "immediately". Perhaps it is better to wait a few days. I don't know the answer, but unfortunately the "contacts to a case" number doesn't tell us.

No, if I were exposed to COVID on April 1 and tested positive on May 30, then the contact would not have been reported.

If the average time to symptoms is 5 days, and a person is infectious 2 days ahead, I'm pretty sure the PCR-RT tests would pick up such an average person around 3 days after exposure. 

A relative who had an exposure on a specific day (and was quarantined by the next day) was told her county wouldn't test her for 5 days after exposure (remember, in quarantine, you can't go get yourself tested; they have to come to you), and in fact didn't test her for 11 days.  Her 14-day quarantine expired before she knew if she was positive (asymptomatic) or negative.
IMO, she should have been tested at 5 days and at 14 days after exposure (if the first was negative and no symptoms have developed).

More testing (say at 8 & 11 days) can give you a better idea of when the disease starts (if asymptomatic) so you can wait out your 10 days in isolation once you get a positive test.  If you test at 14 days and get a (first) positive, you will need to isolate until 24 days after exposure.  That's a long time when maybe you would have tested positive at day 6.

If she tested negative at 5 days and positive at 14 days, she should be counted as one that got it from a contact.  (Remember, she was in quarantine so she wasn't further exposed.)