What is a proper way to consider the supplementary materials as a reviewer? I was chosen as a reviewer for a conference in the field of computer science in which the authors can also submit some extra materials like proofs and additional implementations separately (until a week after the deadline), but their papers should be understandable and self-contained without considering these additional materials.

The paper I’m reviewing has a good scientific contribution and I like the way they tried to solve the problem, but some parts are not so understandable unless you read the additional submitted PDF file. For example, their pseudo-code for their algorithm has some mistakes, but they provide the correct algorithm in the additional material. Also, they provided more implementation results in the extra PDF file, which I think are important to support their claim. The proof and in-detail explanation of their method is also provided there.

The organizers have emphasized that the authors shouldn’t use the additional documents as way to submit a more complete version of the original paper.

So to be fair, if they add some of the parts from their supplementary document to the main paper, then the resulting paper would be perfect and I’d definitely accept it. However, I’m not sure whether it is better to accept it with feedback on the lacking parts, telling them to move these parts from the additional PDF to the main one to make it complete, or to only consider the main paper to be self-explanatory, in that case I’d more likely reject it!
Your job is to provide critique and suggestions by which the authors can improve the paper. The published paper should be self-contained; that does not mean that as a reviewer you should ignore the supplementary material.

It sounds to me like you already know how to advise the authors to improve their paper. I would definitely ask them to make improvements and submit a revision, rather than reject — especially if the paper would be "perfect" with your suggested changes.