The Talmud is POST 70AD. In about 200 AD, the Jews codified their oral traditions in the Mishna. Then, over the next 2 centuries, they added thousands of rules that they called the Talmud. It was an attempt to tell people what God really meant in all of his laws and they got way out of God's intent on many of them.
As a written document, it's post 70 AD. As you say, it was oral tradition before Christ appeared, and he condemned it as false teaching while on earth.
The Mishna is the oral part. The Talmud was added after 200AD. It's entirely man written and it got far afield on what God intended for man.
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