We flew home to NY on 10/30, which was before the test out option was available, so we were required to quarantine for 14 days. We filled out the form with the National Guard before leaving the airport - it was a two page form but they only asked us to complete our name, number and flight number. We never once heard from the department of health, the county, the state... no one. Our quarantine period is over now. So, my guess is that they are focusing efforts on validating testing with those who have gone the route of the new test out option.
It’s my understanding from everything I have read that (in accordance with the new form you have to complete at the airport), you may be required to produce negative results from Florida (or whichever state) within 72 hours of your departure and negative results from NY on day 4 (or later) after arriving, and then you are cleared to end your quarantine. You’d only be “in trouble” if you end your quarantine and can’t produce one of these things, if asked. So there is no expectation of receiving negative results before you travel home to NY.