"If you perform an analysis using ArcGIS Online, the solver references a high-quality, worldwide network dataset stored in the ArcGIS Online cloud and will use ArcGIS Online credits. If you're using your own data, no online credits are used, but you need to associate your network dataset with the project."
I think this is just a matter of unclear text. I will make a note for us to update the tutorial text to make it clearer in the future.
When you create a network analysis layer in Pro, you must choose the network data source you want to use to perform the network analysis calculations. This is the road network the analysis will be based off of. You can choose one of several options:
1) ArcGIS Online - this uses high-quality data that Esri hosts. You cannot edit this data. If you use this service, it consumes credits.
2) Your own network dataset. This is something you make or purchase yourself and have locally on your own machine. It doesn't cost anything to use this.
3) A non-ArcGIS Online portal service - If you have ArcGIS Enterprise and your own portal, you can create your own network analysis services on this portal and consume them from Pro.
The Network Analysis drop-down on the Analysis ribbon shows the current network data source and allows you to change it if desired.
