Correct. I needed to change that ref line on the tie slope. I wouldn't say it is super common, mostly because I tend to use the side slope command instead of the tie slope now, but it does happen. I cloud delete and recreate the side slope on the new linestring which is not which isn't awful, just seeing if there was a quicker way.
I think there is also value in knowing what linestring a tie slope is assigned, which you cannot determine until you edit said linesting.