Why do people have different personalities when speaking different languages? Edit: This study is much more relevant in terms of the question. 

This study suggests (according to article linked below) that a multilingual person can have multiple personalities, each tied to one of the languages that he or she speaks.

Here's an article about the study. 

One personality may be active when the person is interacting in one language, another when interacting in another language, etc.

I have seen this phenomena very distinctly in myself.

Why does this happen?
This is a typical example of the misrepresentation of scientific reseach in popular media.

The orignal study concludes that "language effects on cognition are context-bound and transient, revealing unprecedented levels of malleability in human cognition". The word "personality" does not appear in the original paper. Nevertheless the Daily Mail comes to the conclusion that "[s]peaking two languages really could give you a split personality, researchers have found". No, they haven't.

To understand what is going on here, I recommend the following video to you:

https://www.facebook.com/LastWeekTonight/videos/896755337120143/

So what does the study find? It finds that the different grammatical structures of different languages can influence how people perceive the world and process information. (Please note the word "can" here! It does not always happen, and only to a small extent.) This is an old hat and called the Sapir-Whorf hypothesis.

As for how this changes the "personality" of multilingual speakers: It doesn't. It changes the information that the speakers use to assess the situation and plan their behavior.