Hi Pete,
Here are some thoughts/observations...
With Allow splitting without a selection unchecked, the Split tool will only split the feature that is selected. The feature that will be split will show up in the Split tool's selection tree. The layer's display field property is used to control what attributes show up in the tree (based on a field or expression). So in this screenshot, Line B should be the only line that is split:
Just an FYI - here is where you control the layer's display field or expression:
In the above case, the Name attribute is my display field and my lines have name attributes of Line A and Line B.
Regarding the wrong feature being split: The bottom line is if you have Allow splitting without a selection unchecked, and you select 1 feature and it shows up in the selection tree. Only that 1 feature should be split. If this is not the case, we need to investigate it.
However, since you said...
"Example of 2 polylines and I want to split only A and not B, however when hovering over the
intersection, it shows Line B will be split and not A."
...this leads me to believe you are relying on the Snap Tip to tell you what is going to split. The snap tip shows you what layer and snap agent you are snapping to. This would allow you to snap to another layer while digitizing the cutting line. More on snapping in Pro: Configure snapping—ArcGIS Pro | ArcGIS Desktop
Regarding splitting at an intersection: In 2.5 (coming soon), it will be much easier to split a line at the intersection of another line. We made an improvement for this scenario. You will be able to select the line you want to split, and as long as the intersection snapping agent is enabled, be able to click once:
Thanks,
Scott