I think this is due to the difficulties of navigating the atlas as much as anything (depending on where you come from, clicking on something with the same or similar name can get you somewhere quite different, which is confusing) but I did just manage it...
1. Search for Crested Tit
2. Click on "view map" under the occurrences record map (even though you are already looking at a map ;))
3. Click on a record square (e.g. the one in Suffolk)
4. Click on "View Records"
Here comes the most confusing bit... this zooms you into the record, but if you look above the map that shows you can click on the records tab.
5. Now click on "view record" in this tab (NB record is singular this time!)
6. That takes you to the occurrence record page https://records.nbnatlas.org/occurrence … 5c4059a8b8
7. Top left it says Contact Curator.
8. The email bit doesn't seem to be working but at least you have a name and an organisation and you could go and do the rest outside the Atlas!(Edit just seen Jim's post - clicking on where it says email does indeed work, but needs a redesign to make it more obvious please.)

I kept getting stuck at step 4 and clicking on the map to View records which takes you back to the same page/map tab. I can understand why (there might be more than one record at the grid square) but I think "View Records" should default to the records view not the map view to make getting info more intuitive.