Thanks for your replies! In the end the Delta app showed both legs as part of the same journey, so I was satisfied that there wouldn't be any problems, and indeed there weren't any.

As an aside, what actually happened was that I had correctly bought a single through ticket in Premium Economy from the travel agency, but in September the IND-ATL leg was retimed by a few minutes, and for some unfathomable reason this made the travel agency downgrade my ATL-LHR leg to Economy. This is why my ticket became split - first leg Premium, second leg Economy - but the change notification email from the travel agency and the updated itinerary both showed the ATL-LHR as unchanged and my seat number in Premium Economy as confirmed. I only found out about the downgrade when it was time to check in and my seat number suddenly changed to an Economy seat, and obviously the travel agency were completele useless when I tried to get help from them.

This was the time first time ever I use a travel agency, and I only did it because of work policy, so I hope this incident will allow me to go back to booking directly with the airline again...