I am experienced presenter, my job is to show presentation, organize educations and trainings to different people, with different personality traits in different situation. Until now I collected more the 700 hours of presentation and more then 120 hours of presentation education. In the beginning I had also that problem, but I overcome it by exercise. Now I am completely relaxed when present.
In my opinion cause of this is social anxiety in self presentation:
Here is one research, but I am sure you can find several more if you look to literature section.
Social anxiety, self-presentation, and the self-serving bias in causal attribution .
Also people get aroused because if they think that other judge them, especially if they do not present a lot... here is model how people conclude others judge them
Mood and judgement: The affect infusion model (AIM) 
EDIT: In this case 'fast talking' is indicator of public speaking fear, so you cant using 'public speaking fear' as cause of 'fast talking' because it will be circular definition. Here is a try to explain this in S-O-R paradigm:
State anxiety patterns for public speaking and the behavior inhibition system 
I don't know exactly what is happening in brain but I assume that something is happening in giri of the hippocampus (working memory) which is overloaded with information of judging environment and accommodate presentation, but also have significant role in speech production.