Add a Plain Effector to the Cloner for the thorns, set Parameter for the Plain Effector to only Scale>Uniform Scale>-1, then add a Linear Field and make it fairly narrow.
I have assumed you’re using Start or End Growth for the animation of the Sweep Object/branch:
If you want to use Align to Spline you need to use basic XPresso. Add the Align to Spline tag to the Linear Field and add the spline use for the Sweep Object into the Spline Path (under Tag tab for the Align to Spline tag), then right-click the Growth of your Sweep (under Object tab for Sweep Object) and choose XPressions>Set Driver then go to the Align to Spline tag (under Tag tab for Align to Spline tag) and right-click on Position and choose XPressions>Set Driven (Absolute). If you’ve keyframed the growth parameter and the same spline is used for both the Sweep and Align to Spline tag this should now work.
As an alternative in this case, you could easily just manually keyframe the movement of the Linear Field in time with the spline growth instead.