In 6.5 tagged an asset and then i tried to go to the sites console and search for particular term. I presume this omnisearch from sites console should automatically also bring up tagged assets as well as pages?
As per the screenshot highlighted above, this "pipeline board shorts" is not an asset but a page which is stored in crxde as cq:page type. To get the asset in your search result, you need to search for assets using the Omnisearch field at the top of the Experience Manager web interface. Go toAssets>Filesin Experience Manager, click search icon in top bar, enter search keyword, and press return. Alternatively, use the keyword shortcut / (forward slash) to open the Omnisearch field.Location:Assets is pre-selected to limit the searches to DAM assets. Experience Manager provides suggestions as your start typing a search keyword.
Use theFilterspanel to narrow your search by filtering search results based on the various options (predicates), such as, file type, file size, last modified date, status of asset, insights data, and Adobe Stock licensing. See  for more details.