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You're not seeing "fighting" because there is no feedback between them. The global planner sends things to the local planner and it makes the judgement call about what to do.

Keep in mind TEB predates the Smac Planners by ... a decade or so, so it doesn't really know anything about the nature of the feasible path. Its used to working with outputs from NavFn which are infeasible and TEB's job is to make it feasible by those constraints itself -- so that's what its doing but ignoring Smac's requested maneuvers.

This isn't necessarily a problem unless you want it to exactly follow the Smac Planner's requested direction or TEB is oscillating so often that its not making progress. If you want the robot to always just follow the Smac Plan, you may want to instead just use the RPP controller which will just following the Smac plan exactly and there's no problem because its not a predictive controller that will try to deviate from the path in order to optimize for other criteria.

If you want that predictive behavior in general but not when talking about directional changes, I'd recommend using the MPPI controller that's been released which is a successor to TEB. This will do that for you for the most part currently and I'm working on some branches currently which will provide better enforce doing those path inversions at the same place as the Smac Planner requested very shortly (approx. by the end of the week).