There isn't anything surprising or unprecedented about references to earlier works, and the authors building on earlier models/structures. Additionally, not every article (in any field) is going to be pedagogic. While that could be due to the author writing style, it is not always possible to keep everything at a very basic level too. This is true, in particular for the stuff like letter publications, or rapid communications, where there are limits on manuscript length. Also, when there are existing pedagogic review articles, or otherwise detailed accounts which could pass off as pedagogic, authors generally tend to avoid a detailed presentation, simply cite them and get to their main point.
Since you say that
My mentor wants me to thoroughly understand the ideas stated here because we are going to be implementing those soon albeit with modifications.
it is clear that he/she wants you to understand the basics thoroughly, and not just be limited to the arguments presented in the one article you have at hand. So, if this article appears cryptic, you have no choice but to go through the cited ones for clarifications. Try to see if they are less cryptic, it is possible that the authors may have cited a review article of the sorts I mentioned above. That will certainly help. Based on that understanding, when you revisit your particular article at hand, you will understand it much better and better understand what it adds to the subject.
However, if that doesn't work out, and you still find the arguments too cryptic, consult your advisor and explain why you find it cryptic, which arguments are not transparent etc. It helps to carry along with you the attempts you made towards understanding it yourself, so that he/she knows you are not asking to be spoon-fed. Once he's convinced that you made an effort from your side, he will generally point you towards other articles which could clear up the specific point for you.
I mean, there is no other choice. There is no way you can gain anything out of this collaboration, or implementing anything, unless you are clear about what you are doing.