First, the quantity indicator. Some float indicators are set so that even when the tank reads empty, there is still soome fuel left in the tank. Thus, at empty, you may till have 30 gallons or so in the tank, meaning with a 250 gallon tank, 1/4 burned would mean about 55 gallons burned. 250-30=220, 220/4=55.
Is it possible that you could have burned 55 gallons iin five days? Definitely.
First, if this was the first time heat was put on the house, the house was cold-soaked. So you're not just heating up the air in the house, you're heating up the entire structure.
If you look at the spec plate on the oil burner there should be a "GPH Fire Rate" or something similar. If you have a resonably efficient burner, the rate should be in the vicinity of 1 gallon per hour. To burn 55 gallons your burner would have to be firing an average of 11 hours per day over those five days. Is that possible? While it is a lot, in a cold-soaked house I suppose it is possible while the house is being brought up to thermal equilibrium.
Monitor the consumption over the next few weeks. Your true indication will be the next time they fill the tank, as that will give you a better idea of the quantity consumed since the first fill-up.