It's my understanding that the spikes are associated with earlier events than the two-ish week single infection incubation period because for the case spikes, you have to have a few rounds of infection aka exponential growth before the infection rate impact makes a blip.
As in: If you got 10k new cases in mid/late June, it's not "because" 10k people got infected at one event in early June, but because 10k ppl got infected in early June from 5k people who got infected in late July from ~3k people who got infected in early July from ~1k people who get infected in late May from one event.
Note: Specific numbers pulled out of my ass as an easy way to convey the idea.