It depends on the app. Most of them require that you sign in through Google or Facebook when you purchase. They are then tied to that account and you can install them again for free, even on a new iPhone. I have bought a couple that are tied to that phone and you have to pay for them again before you can install on a new device. MiVTones (video ringtone app) is the only one I can think of. I also had to pay for iRealSMS again, but I think that was just a glitch; most people only have to pay once for it.
I have never had a sign in with Facebook sign come up whilst in Cydia. It may be because I linked my Google account the Cydia as soon as they opened the store. I only ever get Google and Amazon, then I pay via paypal. I don't use Facebook anyway, but thanks for the heads up.