Yes the this the expected behavior, let me precise how the Map Tour data are saved:
- Title/description of each point, as well as the marker color are saved as attributes
- The images are stored as Feature Services with attachments
- The tour title/description and other information like the header logo and links are saved in the web mapping application
- The tour point order and visibility are also saved in the web mapping application (ordered array of the features object id)
The first two group of information are easily editable through Map Viewer for example. The later two are not editable in any tool except the Map Tour builder. If you look at a map tour web mapping application item in ArcGIS Online Assistant you will be able to see and edit those json configuration.
Storing the tour point order in the web mapping application has a lot of advantages for data maintenance but I understand that if you are using the webmap outside of Map Tour for other purpose this is not ideal. If that's what you want to do, I think you will have to use a Desktop tool to physically change the order of the points in the layer.
