Should I (as a reviewer) ask an author to cite my work where I proposed a core hypothesis, when they have already referenced other points?
Think about what would be appropriate if you weren't the author? I think the fact that you are both reviewer and author of the original idea is in some sense a distraction from the main issue. I.e., that whether the author should cite a specific work or not should not be affected by who is reviewing the work. Of course, in reality, authors are intimately familiar with their own work and also have incentives to obtain credit and more citations. Some reviewers are also concerned about the conflict of interest and the power imbalance, or even in maintaining blind review. But ultimately, if you can answer the question of whether the citation was needed had you not been the author, then you probably have the answer to your question.

So, does an author need to cite a reference where a hypothesis was proposed where the author's study pursues that hypothesis?

In general, this would depend on the circumstances. 


Novelty of the hypothesis. If you were the first person to propose the idea, then this suggests a greater degree of novelty. Alternatively, if many papers touch on the idea, then there's less need to cite.
Intellectual insight to identify the hypothesis. If the hypothesis required a degree of insight, then it is more appropriate to cite. For example, suggesting that X may be related to Y or that more longitudinal research is needed are generally ideas that don't need a citation. 
Were the authors actually influenced by the idea. If the idea is a fairly natural extension of the literature, then the authors may have independently come up with the idea. this also speaks to the point that the idea may have required less insight and novelty.
Degree of alignment between idea and their implementation. In most cases, research involves many choices. The expression of an idea can also involve a degree of creativity. Thus, the more the idea is aligned with how you expressed it, the more it is worthy of a citation. 
Do the authors claim that no one has proposed the hypothesis before? If so, then this is clearly wrong, and needs to be changed by either removing such a bold claim or adding a citation.


Overall, whether a previously proposed hypothesis needs a citation depends on the details of your case and your field.

Speaking from a behavioural sciences perspective, I tend to think that many hypotheses do not need specific citations to references where a similar hypothesis was put forward. Discussion sections often are typically not the core contribution of a paper. The empirical study and their results is typically the main component. Discussion sections often include proposals for future research that put forward various ideas that could be tested in the future. Many ideas are relatively trivial to put down on paper (e.g., mediating and moderating variables; suggesting particular studies using particular methodologies). In many cases, the contribution of a study is less in proposing the hypothesis, and more in the collection of data to examine a research question, and the rigorous assessment of what that data means.