The address you tell your company has nothing to do with your legal requirement to pay state income tax.
Start by reading the PA tax site on residency and domicile.
https://www.revenue.pa.gov/TaxTypes/PIT/Pages/Determining-Residency.aspx
Your domicile is your permanent abode. You can only have one domicile at a time. Part of changing your domicile (permanent abode) is your intention. It is possible that you could intend to move to PA permanently, and thus change your domicile, but then change your mind and change your domicile again to move back to Texas. It is also possible to move to PA for a trial period, where you do not intend to change your domicile, at least at first. However, if you physically live in PA more than 184 days, you will be a statutory resident of PA even if you have not changed your domicile.
Now, the general rule is that if you are temporarily living and working in Philadelphia, you will owe Philadelphia city and state tax on all your income earned while living or working in Philadelphia. This would be reported on a non-resident tax return. If you change your permanent residence to Philadelphia, or if you are living in Philadelphia more than 184 days of the year, then you are either a permanent resident or a statutory resident, and you report and pay Philadelphia income tax on all your world-wide income for the year, even if the income was earned or paid in some other state. If you change your permanent address in the middle of the year, you are a part-year resident starting on the date you change your permanent residence.
So let's suppose you move to Philadelphia with the intention that it is a trial period, and you do not give up your Texas domicile (you keep your home, keep your lease, keep your voter registration, etc.). You will be required to file a PA city and state non-resident tax return to report and pay income tax on all your income earned while physically living and working in Philadelphia, even if you did not change your permanent address and even if you don't tell the company to withhold PA tax. If the state finds you physically living in PA, they will tax you, and you may owe penalties and interest if you don't file and get caught later.
Then at some future time, you move back to Texas. Since you never changed your permanent residence/domicile, you stop paying PA tax since you are not working in PA.
Or, at some future time you decide to make PA your permanent home, and you take steps to abandon your domicile in Texas (by selling your home or renting it, breaking your lease, changing your voter and car registration, etc.). From the date your intention changes, you are now a resident of PA and file a resident tax return.
