You need to replay all 3 games and maybe read s couple books to understand it.
Revan didn't willingly or intentionally turn to the dark side. He fought the mandalorians, thats what he believed was right and just and the duty of the jedi so he did it. Through the war he found clues and eventually proof that some sith force on some forgotten world in some distant part of space had manipulated the mandalorians to attack the republic. Se when the war was done he took his best friend and a few ships full of fighters loyal to him out in search of this mysteriously sith empire.
The emperor promptly captured both revan and malik and, under his sway sent them back as sith with the intention of doing as much damage to the republic as possible to soften them up for the sith invasion.
There was no secret Revan plan to strengthen the republic or anything like that. It is clearly explained.
What Kreia says is wishful thinking on her part.