I have seen this under two circumstances.
Pet urine that was watered off the plant and into the ground before it burned the grass blades. Urine is urea which is nitrogen.

Another is when someone was showing an organic fertilizer using rabbit pellets. Rabbit food is alfalfa and/or grain which breaks down to nitrogen and some plant growth hormones.

Fairy rings and I believe Necrotic spot can be the cause of odd greening I believe. Usually also has an area of grass that isn't doing so well also in the middle or on edge.

From the photo it is hard to tell. Looks more like dog spot.

It does look more like dog spot or an accidental fertilizer drop than anything else. I wouldn't be inclined to worry about it unless it gets worse, lightens out in the center of a ring, or kills the grass.

Since you just planted, that might just be an area of particularly deep or rich soil and the grass has simply developed a little faster there. See if it evens out by late spring. Early on, I had a few patches that, insistently, looked better and developed faster than anything else. The rest caught up eventually.

You know, that area was pretty bare, and I overseeded. There are a few other areas like that in my yard--the initial seeding didn't grow much, and I added more seed later. I wonder if that made a difference.

Much of the other new grass in my lawn is yellowing or browning, and I think it's because of a soil problem. Some grass in other areas of my yard never really grew much. Would fertilizing again be a bad idea? Would a soil test be a better idea to start with?

Sounds like a soil test is definitely in order! Throwing more fertilizer (general blend or starter) or blindly adding lime/gypsum or anything else to try to balance out primary or secondary nutrients could also throw off your balance further.

You want to make sure you haven't fertilized in a few weeks before your soil samples. Read up on technique (many samples, selecting only the soil at around the 4" depth or so)

Soil test. It's pretty late in the year (or early, I guess) to be feeding. The grass simply isn't that hungry in January.

+1 Boat. Don't blindly throw resources at the soil (nitrogen being an exception, always target the grass' preferred amount of N per year without consideration of any other resource).

Testing can be thrown off by application of some things, but a high nitrogen fertilizer is safe. Even if the place you choose (like UMass) tests nitrogen, we ignore it. It varies by moisture level, soil temperature, and time of day--and the actual number doesn't matter.