So I finally got the issue resolved with the help of an ESRI tech. Essentially you need to "update indexing" for the open data site with the wrong "found in" tag information. You can do a soft update (organization's open data page>"data" tab>click "update index"). If this doesn't work then a hard reset of the site is the next step. To do this follow the steps below:
1) From ArcGIS Online open the group designated as open data (In case of multiple groups, follow these steps for all the groups)>Edit.
2) Make group private from public>Save>Refresh page>Edit>Make Group Public again>Check the'Designate as available for use in Open Data sites'> Save>Refresh page.
3) Open Group Manager page of the site from Admin page of Open data site>Select the open data group again.
*** Note, both methods might take some time to take effect- meaning the tag changes on the data-sets can be slow to show up, so be patient ***