In this figure a network is shown with it's mouths, nodes, flow direction and a secondary dataset indicating the location of a canal.  It is clear that there are 2 channels feeding the canal.

The same network is shown but the order the polylines were digitised are marked by the numbers. The upstream ID algorithm will start processing each ID in this order. Do the polylines above node A belong to catch 1 or 2 and do the polylines above node B belong to 1, 2 or 3?

With force longest route TURNED OFF the results are as below, this is clearly not correct (but can be useful in identifying network errors).

If you were using distance to mouth in your analyses then a survey site located anywhere upstream of A would be giving a false value (yet it drains to an acceptable mouth).

With force longest route TURNED ON the results are as below.  These results make much more sense, the polylines upstream of nodes A & B are draining to the mouth furthest away.

Distance to mouth would be more meaningful in your analyses.