You are dead wrong, the incubation period is 5.2 days with a 99% range of 2.1 - 7.2 days so please lets make sure we are dealing with the facts as they are not as you wish them to be.
I stand corrected. Even so, most mask mandates are very recent and hardly ever enforced.
Correcting for this aspect of the data seems to be something that is often overlooked in recent research. I don't see from a quick review of the JAMA article that they considered that aspect of the data. The effect of the time delays can be seen in the more detailed modeling and analysis presented by the R(t) research team. Their data and analysis for Massachusetts, available here seems to suggest that the overall rate of infections peaked on April 1st in Massachusetts. I would expect that the peak for health workers might ordinarily lag that of the general population since they have a risk both from their general exposure and a higher risk from at work exposure to COVID-19 patients. The latter risk arrives a few days after the patients themselves became infected, as you noted.
Common sense tells us using masks in a hospital setting is a good idea. I would hope that we might see reductions in all airborne diseases among hospital patients as a result. But separating the effect of mask wearing from, for example, next to no contact with other people outside of the hospital is very difficult statistically.