To "spew" literally means to vomit, or generally to pour out a large amount of something in an uncontrolled way. It is a somewhat negative term. If we say that a volcano "spewed" lava, we don't think that an erupting volcano is a good thing!
An angry person, who is completely out of control and yelling bad words, might be said to be "spewing bad words."
Here, to "spew forth warnings" means to give far too many warnings, in an uncontrolled and thoughtless way. There is a strong suggestion that the warnings are exaggerated propaganda.