Humidity domes simply keep the medium from drying too quickly when you are using heat mats to aid germination. Heat mats are designed to raise the temperature 10-15 degrees F. above room temperature (to around 80 degrees) and this aids in germination and root developement. Humidity is not so much a factor in germination as root zone temperature is.
Be cautious when using a humidity dome because the medium can also become too wet which will actually slow root growth from lack of oxygen or create fungal problems. In my opinion, humidity domes and heat mats are really only useful for cuttings because they have no intention of forming roots and you must make every effort to force them to create them via rooting hormones, heat mats, humidity domes, etc. The tap root of a seed on the other hand intends to form roots and will even without the aid of a humidity dome.
Once the seedlings have there true leaves (first set of 1 finger leaves above the cotyledons) then remove the humidity dome.