Actually if you take a look at the NYS Department of Health report, you'll find that it was actually nursing staff that correlated with the peak number of deaths by covid in the state. It had nothing to do with Cuomo's policy.

It even says here:

"It is likely that thousands of employees who were infected in the mid-march transmitted the virus unknowingly— through no fault of their own— while working, which then led to resident infection."

And again here:

"A casual link between the admission policy and infections/fatalities would be supported through a direct link between the two, meaning that if admission if patients into nursing homes caused unfection— and by extension mortality— the time interval between the admission and mortality curves would be consistent with the expected interval between infection and death. However, the peak date COVID-positive residents entered nursing homes occured on April 14, 2020, a week after peak mortality in New York's nursing homes occured on April 8, 2020. If admissions were driving fatalities, the order of peak fatalities and peak admissions would have been reversed."

https://www.health.ny.gov/press/releases/2020/2020-07-06_covid19_nursing_home_report.htm