What are omics journals?
Nature Genetics is a reputable journal that might publish papers in the category of "genomics," which itself is a subset of "omics." Broadly, omics encompasses the quantification and analysis of various biological components – for example, metabolomics uses LC-MS systems to quantify different metabolites (e.g. tacrolimus degradation products for therapeutic drug monitoring in kidney transplant patients). Genomics analyzes the genome, which includes all the genes we have. 

OMICS Publishing Group is considered a predatory publisher due to an apparent lack of legitimacy in their peer-review process, excessive publishing fees, and fraudulent behaviors as described in Predatory Publishing – Experience 
with OMICS International (Masic, MED ARCH. 2017). However, Genome Research is published by Cold Spring Harbor Lab Press, which is from a legitimate institution.

Searching for "genome research" "omics international" brings up OMICS' Journal of Genome, Human Genome Research Articles page, and Genome Research review page, so I don't think they have a journal called Genome Research.

Your mentor is asking you to review articles from genomics journals like Genomics, Cytogenetic and Genome Research, Genome, Nature Reviews Genetics, BMC Genomics, Journal of Human Genetics and others that you can easily find.

A final aside: Last November, the FTC won an initial court ruling against OMICS International for their deceptive practices. Do your due diligence as you complete your literature survey and stay vigilant against unethical and irresponsible publishers.

These topics are relevant to my home institution (University of Colorado): Jeff Beall was sued by OMICS for raising these allegations several years ago, and I just watched Eric Green (director of the NIH Human Genome Research Initiative) speak at my program's national conference last Sunday.