As for the distance travelled,
The needle stood stiff and proud at the hairline whose figure read 300,000 parsecs.
Unless the dial lied, they had travelled quite a distance.
So the only option is that Asimov chose to ignore it. He left the precise method of travel vague enough.
As Dr. Alfred Lanning states:
"From a scientific standpoint the situation, while not entirely clear, is subject to intelligent analysis. The question of interstellar travel under present conditions of physical theory is... uh... vague. The matter is wide open -- and the information given by Consolidated to its thinking machine, assuming these we have to be the same, was similarly wide open. Our mathematical department has given it a thorough analysis, and it seems Consolidated has included everything. Its material for submission contains all known developments of Franciacci's space-warp theory, and, apparently, all pertinent astrophysical and electronic data. It’s quite a mouthful."
Also, Powell and Donovan die during warp, coming back alive once arrived. Who knows what strange mechanisms may be at work that keep time from dilating and causality from being violated.
How does “warp drive” not violate Special Relativity causality constraints?
This question on the Physics Stack shows that physicists don't yet agree on what happens, either.