Help!! So, my old carpets were lifted to reveal original oak wood floors but about 1/4 of the room had water damage. I hired someone to match the old floors and install them, but they didn’t do any staining or matching, rather just installed planks that were the same size. (I was a little bummed- they also didn’t match the style the old floors were installed… They went with a more recent style: the old planks have a little space between each piece, likely from years of use; The way the new ones were installed they are so tight together that you wouldn’t know they were separate planks of wood’s aside from the different grains.) anyhow, I tried to make the match the old floors by using different types of stain. After six color tries, I thought I had it right. Waited more than the 8 hour setting time and then I started to apply the polyurethane satin finish. All was looking good as I spread it across all planks, which darkened a little as the coating went on. But then when, I reached the newer planks, panic: they did not darken with the polyurethane coating. So as the polyurethane coating went on, they were a completely different color. I frantically tried to wipe off whatever polyurethane was on the newer planks, and quickly put on a coat of varnish. I likely did not get all polyurethane off for putting stain on. Did I totally screw myself? Will a final polyurethane coat even bind to this? For the money they spent, I worry I see a large area rug in my future... Any suggestions on what to anticipate?

It may be that your old flooring shrunk after it was installed, leaving gaps. It could have been stored improperly as the house was being built, picking up moisture from the air that left the wood later causing some shrinkage. If you would like to compare installation differences, measure across five, ten or twenty board widths and see how close to the actual width of what the boards would have been direct from the mill, when they were manufactured. The older part of the floor will probably be more than the actual widths would have been because boards swell when they absorb moisture from the air. They will then shrink, leaving gaps as they become dried out, again.
New wood will darken with exposure to light over time. They may always be a little bit lighter, unless you treat the new planks a little differently, if you use a completely clear finish that doesn't amber like the older oil based varnishes. Over time the new wood will become more like the older wood. Since you stained the wood, this will help a lot. Sunlight is the most effective way to help blend the new and old together.