I just took extract from your statement above:
I have frequently worked ...in other states ...I was not required to pay or file an income tax ...for either state.
If you are working in the state - the income is considered from sources in this state - and in general - if the state has income tax - your income is subject of such tax regardless if it is paid to you on 1099 base (self-employment contractor) or W2 base( employee).
If you inform your accountant that you worked in the specific state - he/she would tell you about such requirements.
As there is no any records where did you actually work - neither NC nor PA DOR are looking for you. Generally without knowing the situation - it looks as all work was done in your FL location.
That is my view on your situation.
For an employee - the situation is different - the company should register in the state it has employees and is obligated to pay FUTA and SUTA taxes.
They also are required to track your work locations, withhold and remit employment taxes and report that on W2 form.
There is no room to escape from state tax liability as it is in self-employment case.