>> Failure to cite relevant research is a reason to reject a paper from a conference but that's not the job of an internal review.

The done thing is generally for the reviewers to suggest additional references to improve the paper. If any mention of related work is entirely missing, then that's another matter, but a reviewer thinking that the authors should cite a particular piece of work (e.g. the reviewer's own paper) is not normally something that could lead to outright rejection.