This seems like it could be a bug of some kind. When I load the map and open the "Configure Popup" menu, it sends a GET request to the service to return the feature attributes.
When the map is clicked, it sends a POST request. It does eventually return the data, but takes a long time. I watched the network traffic on a couple other basic layers as well as attribute-join layers, and none of them send POST requests, just this one.
In Classic, however, the GET request is sent when the layer initially loads, so the data is "already there", as opposed to being fetched upon clicking the feature.
I don't know that this gets you any closer to solving the issue, but could be something for Support to look into further. I have no idea why your service in particular would exhibit different behavior from a variety of test layers.
- Josh Carlson
Kendall County GIS