I live in PA, but worked in Delaware. My W-2 from DE says that nothing was withheld from DE, but that PA state taxes were withheld. Still saying I owe state taxes to PA?

I have never lived and worked in a different state so this is new to me. My W-2 from Delaware (non-resident state) is saying that no DE state tax was withheld, but that $10 in PA tax was withheld (I just started working there in late 2018). Now, when I went to file my PA resident state return, it is saying I owe $10. Do I actually owe this money, even if it my DE W-2 says it was withheld? Also, is there a way to have this automatically withheld for next year, so that I don't end up having to repay the tax when I file next year?