Ancients Cut-scene 1:
Ours was a proud people, and always the strongest. For thousands of years our empire expanded. For so long we could imagine ourselves alone in the universe. For so long never did we encounter advanced life. And we traveled faster and further, spreading in our galaxy and before long we could see the day when our reachable systems would have been exploited. And then there would be nowhere else to go.
And we discovered subspace. It gave us our galaxy and it gave us the universe. And we saw other advanced life. And we subdued it or we crushed it. In months the extermination of billions of years of evolution on a similar but slower path. With subspace, our empire would surely know no boundaries.
Ancients Cut-Scene 4:
There are a few of us left. We know we will soon be gone. And so we can see our fate as others will see it. There will be little legacy. No great expressions of what we once were. Our technology, our achievements if ever they are seen again will spawn none of the awe that filled our conquests.
We know our fate. We are being eliminated. When we traveled subspace, the cosmic destroyers took note.
When we conquered and colonized in galaxies where we had no place the destruction and the anguish and the loss were the clarion call of our doom. And so the destroyers came for us.
So it appears that at first, the Ancients may have used high-sub-light travel to reach their nearby systems, possibly combined with hibernation for the crew. That said, we don't know how long they live as a species, so for them a 50 yr. transit time could be a drop in the bucket, so hibernation may have been unnecessary. Another possibility could be that the Ancients' home system was amidst a tighter star cluster like the Pleiades, reducing the transit time between star systems. The "thousands of years" time-frame for the expansion of their empire BEFORE they discovered subspace, could support the long-duration spaceflight theory.
As for the statements regarding the scope of the Ancients' empire, the quote clearly states "galaxies", plural. However, that could simply refer to the satellite galaxies of our own Milky Way, such as the LMC and SMC. In any case, the distances involved in reaching these destinations, would likely support the conclusion that the Ancients developed a more advanced form of subspace travel to get there.
In the final analysis however, one could argue that whoever wrote the dialogue for these cut-scenes did not have direct access to "canon" info. regarding the established (or inferred) rules of travel and navigation in the game story itself. If they had, they may have limited the context somewhat.