You should apply two coats of primer to "kill" the blue background color. Many interior primers can be tinted to approximate your finish color. This is usually about 50-60% of the final color. Primer doesn't take tint the same as a paint. This will make your painting a lot easier.
An alternative is to use flat paint as your first and possibly second coat tinted to match your finish color. Good flat paint covers well and can seal up the old color.
Go ahead and put another coat of paint on and see what it looks like after it has dried for a few hours.