I don't think it is true that extroverts don't think before speaking. The difference between I/E is that introverts think about what they are saying and extroverts think about how what they are going to say will affect those they are saying it to.

Introverts care less about the feelings and emotions of their co-conversationalists and extroverts are more socially motivated to say nice things that make the group feel good or work better.

I think both introverts and extroverts think about what they are going to say. The question is, what do they tend to say once they've thought about it?