What is the meaning behind his words?

I have been dating a Japanese guy for several months. These days, he mentioned to me the following:
素直でいい子。

I asked him what does he mean. His reply was this:

従順だということです。

I didn't ask him any further questions and explanation about this. So, here I am, with the hopes that you guys here in Japan Guide will enlighten me!

Btw: Our communication is in Japanese only.

Any tips, advice and suggestions are welcome.

He said that you're a tame good girl

Sounds rather condescending to me.

従順 is obedient, submissive, etc.
You will find out what his true character is like, when you challenge him.

Naes and Fluffy, thank you for the replies!

Do his words mean that, if we marry, he expects me to be obedient to him?

Thank you Ay for the reply!

Could this mean that he expect me to be obedient to him?

You can't judge anything from this, really. It's a common expression when jokingly settling a situation where no conflict or sarcasm was done.