Probably not. The instructions to the allocation form Form IT-203-B Nonresident and Part-Year Resident Income Allocation Form (click on link to open up form) requires that "at-home" work days be excluded from days allocated outside of New York. If you see line 1j on the form, this is specifically mentioned. As @Anonymous_ presents with that article, for a day working from home to be considered as not taxable to New York, New York generally considers that such work must be necessary to perform from an out-of-state employee, and not just a convenience to do so. Living over 1000 miles away in Miami does not make working from home necessary by New York's standards. Being required to be in Miami to physically attend to client interests could be.
Based on this, it is unlikely that New York will accept allocating your at-home work from June to October as income not subject to New York tax. Even if you moved, you will still be liable to pay tax on this income as a nonresident.
But you are correct that once you set up a Miami-based office (not at home), this now meets New York's definition of necessary, so going forward, you do not pay New York tax on that income.
@fareedm
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