Assuming you are only getting reliable tests from people who need hospital care, getting sick requires 2-14 days and getting sick enough to go to hospital often another few days. Then another few days for a test turnaround.
So an increase in exposure over May 22-25 wouldn't start showing up until early June.
This graph:
is amazingballs. It shows that Covid-19 in wastewater predict diagnosed Covid-19 cases
by a week with an above 0.9 correlation.
That increase in C19 in wastewater means those people are infected and shedding virus. And it takes a
week after they are shedding virus that some subset of them show up, get tested, and the test results come back.
How long it takes to go from initial C19 exposure to shedding C19 out your bum is another question, but it isn't going to be negative days.
Suppose it takes about 2 days to go from C19 exposure to it coming out your bum. Then it will take 7 more days for you to be diagnosted. Thus a 9 day lag.
May 22-25 is May 31 to 34, aka May 31 to June 3rd.
And like most exponential functions, the cost of the new infections isn't just the new infections, but all of the people they'll infect.