Well it all depend on yourself, whether you want to start your job as being informed through email or wait for the official employment. Below is my own personal experience which quite similiar to you.

Current I working in one of Berjaya subsidiary company, which I also being contact through phone to start my job before I had get to see or sign my employment letter. My employment letter only reach me around 2 week after I started my job. And I started my job at the last week of the month, which my boss want to start immediately because of lack of man power.