Is every post on my LinkedIn account liked by the tribe? 

No, this does not happen automatically. Only the posts of which you put the link in LikeTribe are liked. With all the other posts that you don't put in LikeTribe, nothing will happen.

Is it correct that I have to put the link in the LikeTribe dashboard of every post that I want my tribe to like?

Yes, that is correct. If you want the tribe to like a post, you need to put the URL link in LikeTribe. If you don't do this, the tribe will do nothing with the post. 

Not everyone in the tribe likes the post, how is this possible?

This is done on purpose, so don't worry nothing will go wrong. LikeTribe will like the post with 85% of the people in the tribe. So never with the full 100% of people inside the tribe, this is done to make the behaviour of the tribe seem as human as possible. 

By having 85% of the tribe liking a slightly different group is selected for each post. Because of this, LinkedIn will see it as human behaviour every time and not as a tool.