Uploading under peer review manuscript
It is not uncommon for working papers to be uploaded to academic websites prior to, or during, peer review.  The only possible impediments I can see to this would be if the agreed terms of review of the journal you have submitted to prevent you from doing this (i.e., publishing the draft during review) or if the terms of the institute's website prevent this.  I doubt that either is the case, but if you're not sure, check the terms.