Have you kept the soil damp? Also, what are your low temperatures? Highs in the fifties are actually awfully chill for grass to sprout, so if that isn't the low temperatures, it's going to be a little while yet!

Optimally, keep it damp by watering it at least twice a day. In Arizona, in what's probably drier air than I'm used to, we might very well be talking three to four times per day. We're not saying hour-long watering, just enough to keep the surface damp as the under-soil should already be moist and kept that way by minimal watering (if it does require more than that, certainly do it).

Seed that dries out is seed that's rapidly dying. Fortunately, colder temperatures stall the process, so you might have gotten away with it. Once the grass is fully sprouted, slowly back off the watering to allow the grass to grow new root systems. Once a day immediately, sure. Every other day a few days later, perhaps. Hold that and then try every third day maybe two weeks later. And so on.

Spring seedings are demanding, so you're going to have to continue to irrigate during your probably-long and probably-hot summer. Sorry about that. And, most likely, reseed some as the weather turns to fall to compensate for summer's losses. Spring seedings work best in cool, damp climates, which...well, you don't have anywhere in that state.

Your mix will not survive even if it comes in extremely well. Why? The summer heat will take it out by June. That mix should not even be offered in your area. I realize there are successful stands of fescue in Tucson, but not many, and the effort to maintain them is far too much. You will be better off with bermuda or St Augustine.

What will the lawn be used for? Is it just for looking at, or do you plan to put a table in the middle with chairs all around? 450 sqft isn't much.

Are you willing to water it deeply and infrequently all year long? Deeply means 1 inch all at one time. That might take a couple hours depending on your sprinkler. Infrequently means once a week with temps in the 90s and once every 5 days with temps from 100 to 105. From 105 to 110 you should water once every 4 days. Is that something you can do?