Work Remotely in PA for Company in Ohio - taxed locally?

I work remotely in PA for a new company based in Ohio. I am taxed  where the company resides. I am reached out the HR department and they stated I need to pay the Pay Roll tax which is tied to where I work.   I think this needs to be my home office not where company office is located. 

Also I paid the Ohio state tax for 6 months instead of PA, this was recently corrected.  How would I correct this when its time to file taxes?