I want some vibrant colored perennials that don't spread more than 12-14" that would do well in Fremont, CA (according to zone map on this site, it's zone 8b) in a spot that gets full sun for about 6 hours.

I would like to make a narrow three tiered flower bed with tall purple flowers in the back, then medium height yellow, then low height red, so would appreciate advice on all three colors.

Would Caradonna salvia work for the purple?

I'd like plants that are evergreen and have a long blooming season.

The bed is about 20" deep.

Karen, which direction does your flower bed face? If it is east facing, the morning sun and shade in the afternoon would make it possible to grow some different plants than if for example the bed faces west.

That's a very narrow bed for you to grow three rows of plants in. Be sure to give the plants enough space to expand their foliage. If they can't grow healthy foliage they won't bloom well for you.