I'm sorry that I can't directly help on this. I do not use any of the online programs. I use Intuit's Professional-Level Turbo Tax, which costs me well over $300.
I have no problem in handling clients where they work in multiple states during the year, where they work in one state and live in another, or they move from one state to another during the year. However, I do know what the rules are and also how it is handled in the program that I use; I also know when do do overrides if the program does something I don't want it to do.
But in general there are two possibilities, depending on the state's agreements.
One possibility is full reciprocity, such as people who live in DC, MD or VA and work in one of the other of the jurisictions report all income to their home state and the employer will take out withholding from the person's home state, not the state they work in.
The other is where there is no reciprocity, such as I have a client who lives in LA but works in MS. All income is reported to and taxed in LA. A non-resident return is filed in MS and the tax is computed on the MS income as well as certain prorations of deductions and exemptions. Then there is a credit against the LA taxes for the MS taxes which are paid.
But any time you are dealing with multiple states it almost calls for profesional assistance. If you are comfortable with doing your own return you can do the current year based on the way that a professional handled a prior year return that was similar.