I moved to Georgia in June and my paystub shows my residence as GA but only shows Massachusetts state taxes being taken out. Is that correct? I'm afraid I will be hit with a large Georgia tax bill come tax season.
You are going to have to file part-year resident state tax returns for MA and GA. When you began living/working in GA you became subject to GA income tax. You need to have your employer change the withholding to GA instead of MA going forward.
https://ttlc.intuit.com/questions/1901560-how-do-i-file-if-i-moved-to-a-different-state-last-year
https://ttlc.intuit.com/questions/1901227-how-do-i-file-a-part-year-state-return
Sorry, I should've added that I moved from TN and now live in GA. I've never lived in Massachusetts and I am just a fully remote employee whose headquarters are in MA. My paystub says my residence is GA but the only taxes being taken our currently are for MA. Should I be seeing a line for GA state taxes too?
"Should I be seeing a line for GA state taxes too?"
Yes, ideally. When you became a GA resident, all your income from that point on became subject to GA income tax, regardless of the income's source. If your employer does not withhold GA state income tax for you, then you must make quarterly estimated tax payments to GA. See this:
https://georgia.gov/pay-estimated-tax
Also, if you never physically work within the state of MA, then your work income is not taxable by MA. If you will be working 100% remotely from a GA location, then your employer should cease withholding MA income tax. MA income tax does not apply to non-residents who perform no work within the state of Massachusetts.
If MA taxes were incorrectly withheld from your pay, then you may obtain a refund by filing a non-resident MA tax return, on which you report the withholding but declare zero MA income.
Your employer's location is irrelevant; the issue is where you live and where you physically work.