diff --git a/seaborn/_core/plot.py b/seaborn/_core/plot.py
index c9dc61c8a7..9e4b8ff699 100644
--- a/seaborn/_core/plot.py
+++ b/seaborn/_core/plot.py
@@ -1154,7 +1154,8 @@ def _setup_figure(self, p: Plot, common: PlotData, layers: list[Layer]) -> None:
                 # axis / tick labels can be shown on interior shared axes if desired
 
                 axis_obj = getattr(ax, f"{axis}axis")
-                visible_side = {"x": "bottom", "y": "left"}.get(axis)
+                # This allows correct handling for twin{x/y} axises (GH 3614)
+                visible_side = axis_obj.get_label_position()
                 show_axis_label = (
                     sub[visible_side]
                     or not p._pair_spec.get("cross", True)
@@ -1172,8 +1173,9 @@ def _setup_figure(self, p: Plot, common: PlotData, layers: list[Layer]) -> None:
                     )
                 )
                 for group in ("major", "minor"):
-                    side = {"x": "bottom", "y": "left"}[axis]
-                    axis_obj.set_tick_params(**{f"label{side}": show_tick_labels})
+                    axis_obj.set_tick_params(
+                        **{f"label{visible_side}": show_tick_labels}
+                    )
                     for t in getattr(axis_obj, f"get_{group}ticklabels")():
                         t.set_visible(show_tick_labels)
 
diff --git a/tests/_core/test_plot.py b/tests/_core/test_plot.py
index 5554ea650f..40f281cd71 100644
--- a/tests/_core/test_plot.py
+++ b/tests/_core/test_plot.py
@@ -1124,6 +1124,24 @@ def test_on_axes(self):
         p = Plot([1], [2]).on(ax).add(m).plot()
         assert m.passed_axes == [ax]
         assert p._figure is ax.figure
+        assert ax.yaxis.get_label_position() == "left"
+        assert ax.yaxis.get_ticks_position() == "left"
+        assert ax.xaxis.get_label_position() == "bottom"
+        assert ax.xaxis.get_ticks_position() == "bottom"
+
+    @pytest.mark.parametrize("axis,exp_position", [("x", "top"), ("y", "right")])
+    def test_on_secondary_axes(self, axis, exp_position):
+
+        ax = mpl.figure.Figure().subplots()
+        twinned_ax = {"x": "y", "y": "x"}[axis]
+        ax2 = getattr(ax, f"twin{twinned_ax}")()
+        m = MockMark()
+        p = Plot([1], [2]).on(ax2).add(m).plot()
+        assert m.passed_axes == [ax2]
+        assert p._figure is ax2.figure
+        targetaxis = getattr(ax2, f"{axis}axis")
+        assert targetaxis.get_label_position() == exp_position
+        assert targetaxis.get_ticks_position() == exp_position
 
     @pytest.mark.parametrize("facet", [True, False])
     def test_on_figure(self, facet):