DO NOT FERTILIZE TODAY. The sod was already heavily fertilized before it was cut. That's the last thing they do to the fields they are cutting. Wait until Memorial Day.

Before you water for 10-15 minutes, measure your sprinkler output. The 10 minute rule for new sod/seed works unless you have a high performance sprinkler. Some sprinkler systems can put out an inch of water in that time. All you need to do is mist the surface, not drench the depths. Measure yours with a tuna or cat food can. Put several cans out and see how much water you can get in 10-15 minutes. All you need is about 1/10 of an inch for these initial sprayings. That's just enough to keep the sod from drying out.

Pending the results of your watering system flow test, the schedule you propose is probably a good watering schedule to start with. I've never seen that particular schedule before, but looks good to me. When you cut back on the frequency in the later weeks you should water longer. Before you back off on the watering frequency, double check to be sure the new sod has rooted into the underlying soil. Try to lift a piece. If it seems stuck, then start backing off and watering longer. The idea is to develop deep roots that will resist the summer heat. In the subsequent weeks try skipping a day and see if the grass looks okay. I assume it will be fine. Then skip the next day. On the 3rd or 4th day, try watering for 30 minutes. Eventually you want to extend to the point where you are only watering once a month in the cool months and working your way to once a week in the heat of summer. On the rare, hot, droughty summer you might go to once every 5 days. But you will be watering a full inch (or thereabouts) when you water. You'll have to come to your own timing based on sprinkler output, wind, humidity, soil type, grass height, shade, rain, and a few more factors. During a normal summer I water 3/8 inch per week in my soil and shade situation in San Antonio. With my sprinkler that takes 3 hours. Last summer during the drought I was up to 7/8 inch per week. That was extreme for me.

More questions?