I could imagine a communications breakthough, or perhaps an expansion of a Federation-wide instant communications network to encompass the Romulan border between TNG S1 and FC. But the superquick warp jump to Earth (I find it hard to believe that days passed in that scene break) is a little harder to reconcile, unless the Enterprise-E is significantly faster than the -D.
Umm, that's more an eye-of-the-beholder thing, really. We get no instant communications between Earth and the RNZ, or any other location and the RNZ, in ST:FC. We merely get messages that reach the RNZ after spending an unknown amount of time in transit.
And the time it takes the E-E to get from the RNZ to Earth is never stated. It may be minutes, it may be hours, it may be weeks. All we know is that the same people are at the bridge stations at departure from RNZ and arrival to Earth, but we could say the same about just about any departure and arrival in TOS... The Alpha Shift might have gone to get some sleep a couple of times between those.