Whether you prime before applying texture depends on what you are doing. I will explain the rules I follow concerning priming before texture and provide a few examples.
Primer Before Texture
Primer can be applied before texturing and will help to control the drying of an applied texture. This is usually done when an entire house or room is going to be textured. In this case the primer should have good sealing capabilities and a slight sheen when dry. I often use a primer tinted a light blue. This helps me to see the texture as it is applied.
This method works great with all types of textures on new drywall or plaster walls and ceilings. Another reason to prime first is to help the texture stick to previously painted surfaces.
Small patches, under a foot in diameter, usually don't require priming before the texture is applied. For applying a knock down and brush texture to patches I still prime first. The new texture blends better with its surroundings when a primer is applied.
The reason for this is the patch can and will absorb water from the drywall mud used for texturing the patch. This will cause the texture to shrink. So priming controls the shrinking of the drywall mud.
Primer Before Patching
A primer can also be applied before any patching takes place. This is a good idea if a damaged area is very powdery and weak. Old plaster will benefit the most from pre-priming. Primer will help stabilize an area and provide a sound surface for the patching and texturing.
Additional priming is still needed after all textures are applied and have dried. Priming before texture is a separate step from the painting.