Parrots do indeed produce saliva. They have salivary glands and a system of ducts, like other animals. The difference is in the distribution of these glands. The end of the tongue in (most) parrots is void of glands and is usually dry. The glands are located around the base of the tongue, all around, front and back. There are also glands in the soft palate in the roof of the mouth, near the back.
If the tip of the tongue, where it is usually dry is seen to be wet, there may or may not be a medical reason for it. It may just be that they are massaging the inside of their mouth with the tip of the tongue ( a natural behavior to clean the mouth) and the tip gets saliva on it then.
This cleaning behavior may become exaggerated if there is irritation or inflammation in the mouth, so it is always a good idea to investigate if the tongue seems wet a lot on the tip, or if there is also other behavior that might suggest oral irritation, such as a lot of yawning or mouth gaping or head shaking or pawing at the mouth with the toes.
Amanda does it all the time. IMO most of the time it's the parrot version of "chewing gum".