You have that backwards.

Moral people follow their moral philosophy because they believe it's the right thing to do, whether they are Christian or atheist or neither.

Some moral people also believe God has told them to do certain things, and use those beliefs to help them select a moral philosophy. Those people are moral and religious.
Other moral people don't believe that, and select a moral philosophy without the aid of that belief. Those people are moral and atheist.

Some immoral people believe that God has told them to do certain things. Those people are immoral and religious.
Some immoral people don't believe that. Those people are immoral and atheist.

Incidentally, I know no atheists (whether moral or not) who adhere to the Talmudic version of the first commandment. But then, since you are talking about the ten commandments in a Christian rather than Jewish context, I suppose you don't subscribe to the Talmudic version anyway a. (cf http://en.wikipedia.org/wiki/Ten_Commandments#Two_texts_with_numbering_schemes)

EDIT: I should probably also say explicitly that I don't mean to assert here that nobody follows the ten commandments simply because they believe God told them to... perhaps some people do. But someone who doesn't think the ten commandments are the right thing to do and does them anyway simply because God told them to is not a moral person, but rather a devout or God-fearing person. (e.g., Abraham setting out to sacrifice his son).