For that matter, in the confused nature of time travel, that 'turmoil and conflict' may have been CAUSED by their sending the Super-American back in time - and for that matter, it may have ultimately proved the catalyst that led to the formation of their society.
If the dates seen in the time traveling sequence are indication, the future is sometime in the 24th century. I don't think their knowledge would be that distorted. In fact, it's possible that they knew exactly what was going to happen from their history, so they staged the contact with the processor and instructed Super-American to do exactly what the history says he did - just to make sure the time line doesn't accidentally collapse on itself.