Yes they should follow the jee advanced syllabus.

But there are some topics which are included in only jee mains .

And there are some topics which included in onle jee advanced.and sometimes they give one or two questions from the concept beyond syllabus.

So it is sufficient to follow syllabus if you are well prepared.

Because it will not effect your rank so much because those one or two questions are equally unknown to others also.

Any other query 

Always welcome

Good luck 

Dear Ram,

JEE has never gone out of the syllabus.

They do give some questions which are out of syllabus but with a neat legal right that they put a comprehension type.

So they expect you to understand a new concept which is out of syllabus by reading the comprehension and then the questions asked below.

So, Once you realize this, they do follow their syllabus strictly.

I think it's helpful for you. Be prepare hard,  and feel free to ask anything here. 

Best wishes.