Good classification, poor separation with TSNE/UMAP

I have been working on a classification problem for which I have been able to achieve good results across various classification metrics. I have been careful to ensure that I am not leaking information at any stage in my pipeline, but its always possible that I've missed something. Recently, I ran the data through TSNE and UMAP and found that my classes do not separate well at all. This is surprising given the success of my models. Is this discrepancy an indication that my models are somehow overfitting? Or is it possible that a classification problem is tractable even if TSNE and UMAP have trouble separating classes?