Hi,
I am sorry for my slow response.
If your gene sets are significantly enriched in both up and down DEGs, that means your genes are generally enriched in DEG of that tissues.
I split DEG into up and down so you can break down if your genes are specific to one direction.
You could say, your genes are specific to the tissue you are seeing the enrichment in both up and down DEGs.
This means when those genes are somehow affected, and if some of up DEGs are under-expressed or down DEGs are over-expressed, which can affect the function of the tissue.
This is just one way of understanding the results, of course, the enrichment test itself cannot prove it but I think the enrichment of DEG generally indicates tissue specificity of your genes.
Hope this helps.
Best,
Kyoko