My dad was a used car dealer (owner) of california of 30 years. Yes it is legal, The auction still has the title, the accounts at manheim or similar have probably been paid months ago and the dealer is waiting on the title this can take months oddly enough. They don't let you leave the auction without it being paid for thou. You would still be waiting a month or 2 anyways because they need to put the title in your name anyways which takes time.
As far as a refund, the laws apply here (california) as follows. If you drove off the LOT you have no buy back, if it was delivered by the dealer you have 1 week. Contact the dealer immediately. In texas, you may have as little as 24 hours to return a vehicle. Ask beforehand if the dealership accepts returns. You may be entitled to a full refund; you may have to take a pro-rated reduction for the time you had the car in your possession. Even if you can't get your money back, many dealers will work with you and even offer you a trade-in to purchase a different car. If the car was delivered you have more time.
As for my evaluation, if the dealer has a dealer license.and it should be hanging up somewhere in the general area as per (california and many states) dealer plates, Release of sale etc etc. You should be fine. If you are REALLLY worried. Check the States DMV websites for occupational car license. If they don't have one they are "curbstoning". Curbstoning is when a dealer poses as a private seller to sell a car. By curbstoning, a dealer can avoid having to comply with the same regulations dealers are upheld to. To a buyer this could mean buying a car that has not passed checking tires, wiper blades etc.
If they are legit in the dealer website no need to worry if it doesn't show up after 2 months and SOMETHING is fishy they have a $100k dealer bond usually and contact the DMV can go after the bond. This bond is a form of consumer protection against fraudulent dealers. It is a promise to the obligee that you will adhere to Texas vehicle dealer laws and regulations, and operate ethically. If you are found to be operating unlawfully or unethically, the principal is liable for the full sum of the bond ($25,000).