As ft101 says, those are the times at which the restrictions apply, not the fare. An off-peak day return doesn't have to be purchased in advance - you can buy it on the day, for the same price, from a machine or ticket counter at Edinburgh station.

You should bear in mind that St. Andrews doesn't have a train station, and that the ticket Scotrail will sell you will involve taking a train to Leuchars and a bus from there to St. Andrews (which isn't far).

You might find it more convenient to take a direct bus from Edinburgh to St. Andrews. The X59 bus, operated by Stagecoach, runs every hour and takes about two hours. If you do this, it's advisable to board at the starting point of the bus because it can get very full.