Remote Worker in 3 States — Which State Do I Owe Taxes To?

I publish illustrative scenarios prepared by my practice. All participants and conversations are fictional. The fictional posts are not posts by real users, accounts of client experiences, or reports of actual results.
Illustrative scenario prepared by my practice.
For informational purposes only. This is not legal advice.
Hypothetical question

English isn't my first language so bear with me. I am a fully remote software developer. My employer is based in New York. I lived in New Jersey from January to April, moved to Florida from May to September, and have been in Texas since October. I did not step foot in my employer's NY office all year.

My employer has been withholding NY state income tax all year. My accountant says I may owe taxes to NJ and possibly NY under the "convenience of the employer" rule, but not to FL or TX (no state income tax). This seems insane — I could owe taxes to a state I never worked in?

Has anyone dealt with multi-state tax issues as a remote worker? Do I need to file in all three states plus NY?

Illustrative response

Document everything. I can't stress this enough.

Illustrative response

Have you consulted with a CPA yet? This is complex enough to warrant professional advice.