It sounds like ideal conditions to me. You did a few things that you did not need to and might be a problem, but you can't fault the weather.

When Mother Nature plants grass seed she has bison, cattle, sheep, goats, antelope, deer, etc. run through and knock the seeds off the plants. Then the following animals either walk or trample the seeds pressing them into the surface. They generally don't get worked into the soil or covered with straw. You could have scattered the seed on top of bare soil, rolled it down with a water filled roller, and gotten pretty close to what Mother Nature does. The seed seeds sunlight and still gets moisture from good contact with the surrounding soil.

What you're going to see is the grass trying to come up through the soil and then through the straw. Your next question will be, 'should I rake the straw away and if so, when?' There's no great answer to that question. If you rake it you risk damaging the new grass. If you do nothing then some of the grass under the heavier loads of straw will not come up until later.

Spring is a poor time of year to seed grass. Fall is the best time because the summer weed seeds are not germinating in the fall. Also spring seeded grass has trouble developing strong roots before the summer heat sets in. If you live someplace like the PNW where the summer heat is pretty mild, you have a better chance of making it through to August. If you have some thin spots or get some crabgrass, don't worry too much. You can fix it in the fall for next year.

Here's some more info.

Basics of Lawn Care

After reading numerous books and magazines on lawn care, caring for lawns at seven houses in my life, and reading numerous forums where real people write in to discuss their successes and failures, I have decided to side with the real people and dispense with the book and magazine authors. I don't know what star their planet rotates around but it's not mine. With that in mind, here is the collected wisdom of the Internet savvy homeowners and lawn care professionals summarized in a few words. If you follow the advice here you will have conquered at least 50% of all lawn problems. Once you have these three elements mastered, then you can worry about weeds (if you have any), dog spots, and striping your lawn. But if you are not doing these three things, they will be the first three things suggested for you to correct.

1. Watering
Water deeply and infrequently. Deeply means at least an inch in every zone, all at once. Infrequently means monthly during the cool months and no more than weekly during the hottest part of summer. Do not spread this out and water for 10 minutes every day. If your grass looks dry before the month/week is up, water longer next time. If that does not work, then you might have to water more than once per week during the summer's hottest period. Deep watering grows deep, drought resistant roots. Infrequent watering allows the top layer of soil to dry completely which kills off many shallow rooted weeds.

You will have to learn to judge when to water your own lawn. If you live in El Paso your watering will be different than if you live in Vermont. Adjust your watering to your type of grass, temperature, humidity, wind, and soil type. It is worth noting that this technique is used successfully by professionals in Phoenix, so...just sayin.' The other factors make a difference. If you normally water 1 inch per week and you get 1/2 inch of rain, then adjust and water only 1/2 inch that week.

2. Mowing
Every week mulch mow at the highest setting on your mower. Most grasses are the most dense when mowed tall. However, bermuda, centipede, and bent grasses will become the most dense when they are mowed at the lowest setting on your mower. In fact there are special mowers that can mow these grasses down to 1/16 inch. Dense grass shades out weeds, keeps the soil cooler, and uses less water than thin grass. Tall grass can feed the deep roots you developed in #1 above. Tall grass does not grow faster than short grass nor does it look shaggy sooner. Once all your grass is at the same height, tall grass just looks plush.

3. Fertilizing
Fertilize regularly. I fertilize 5 times per year using organic fertilizer. Which fertilizer you use is much less important than numbers 1 and 2 above. Follow the directions on the bag and do not overdo it (unless you use organics in which case you may overdo it without fear of hurting anything).

At this point you do not have to worry about weed and feed products - remember at this point you are just trying to grow grass, not perfect it. Besides once you are doing these three things correctly, your weed problems should go away without herbicide.