Q. Do I now have to pay California income tax?
A. Yes.
Q. if so, is it for my entire paycheck for both incomes?
A. No, just the income from the 2nd job.
The general rule is that your military pay is subject to taxation ONLY by your State of Legal Residence. Income from a second job is subject to taxation by the state where you are live and work – which for most servicemembers will be the state where they are stationed.
The fact that you will be physically working in CA, despite a Florida or Pennsylvania employer, means that income is subject to CA income tax.