In the scene after Zefram's ship goes to warp, when the ship is being turned around to return home, Cochran remarks "Is that the Earth? It's so... small" He wouldn't have been able to see it, provided the distance the ship just flew. Warp 1 is the speed of light and in a 1 minute flight, the Phoenix would have travelled over 10 million miles - at that distance the earth would just appear like a bright star.
When the Phoenix turns, the Earth appear to be about a third of a degree across. Four and a third million miles, or 23 light seconds. I figure that in the 55 second of screen time the Phoenix didn't just go straight out and then stop, but was traveling in a curve.
Either than, or some of the scenes with the interior of the Phoenix, and the interior of the Enterprise were occurring concurrently within the movie's timeline. The Phoenix simply wasn't at warp for a near minute, but only a couple of dozen seconds.