diff --git a/bindings/pydrake/systems/meshcat_visualizer.py b/bindings/pydrake/systems/meshcat_visualizer.py
index 0711a3126cee..02aa2d8de547 100644
--- a/bindings/pydrake/systems/meshcat_visualizer.py
+++ b/bindings/pydrake/systems/meshcat_visualizer.py
@@ -250,8 +250,10 @@ def __init__(self,
         self.set_name('meshcat_visualizer')
         self.DeclarePeriodicPublish(draw_period, 0.0)
         self.draw_period = draw_period
-        self.reset_recording()
+
+        # Recording.
         self._is_recording = False
+        self.reset_recording()
 
         # Pose bundle (from SceneGraph) input port.
         # TODO(tehbelinda): Rename the `lcm_visualization` port to match
@@ -382,41 +384,53 @@ def DoPublish(self, context, event):
             # The MBP parsers only register the plant as a nameless source.
             # TODO(russt): Use a more textual naming convention here?
             pose_matrix = pose_bundle.get_transform(frame_i)
-            self.vis[self.prefix][source_name][str(model_id)][frame_name]\
-                .set_transform(pose_matrix.GetAsMatrix4())
+            cur_vis = (
+                self.vis[self.prefix][source_name][str(model_id)][frame_name])
+            cur_vis.set_transform(pose_matrix.GetAsMatrix4())
             if self._is_recording:
                 with self._animation.at_frame(
-                    self.vis[self.prefix][source_name][str(model_id)]
-                        [frame_name], self._recording_frame_num) as frame:
-                    frame.set_transform(pose_matrix.GetAsMatrix4())
-                self._recording_frame_num += 1
+                        cur_vis, self._recording_frame_num) as cur_vis_frame:
+                    cur_vis_frame.set_transform(pose_matrix.GetAsMatrix4())
+
+        if self._is_recording:
+            self._recording_frame_num += 1
 
     def start_recording(self):
         """
         Sets a flag to record future publish events as animation frames.
-        Note: This syntax was chosen to match PyPlotVisualizer.
+
+        Precondition:
+            This must not be recording.
         """
+        # N.B. This recording API is intended to match PyPlotVisualizer's.
+        assert not self._is_recording, "Must NOT be recording"
         self._is_recording = True
 
     def stop_recording(self):
         """
-        Sets a flag to record future publish events as animation frames.
-        Note: This syntax was chosen to match PyPlotVisualizer.
-        """
-        self._is_recording = False
+        Stops recording and publishes animation to ``meshcat.Visualizer``.
 
-    def publish_recording(self):
-        """
-        Publish any recorded animation to Meshcat.  Use the controls dialog
-        in the browser to review it.
+        This animation can be seen using `self.vis.render_static()`, and you
+        can browse the animation using meshcat's controls in the browser
+        widget, under "Animations > default".
+
+        Precondition:
+            This must be recording.
         """
+        # N.B. This recording API is intended to match PyPlotVisualizer's.
+        assert self._is_recording, "Must be recording"
+        self._is_recording = False
         self.vis.set_animation(self._animation)
 
     def reset_recording(self):
         """
         Resets all recorded data.
-        Note: This syntax was chosen to match PyPlotVisualizer.
+
+        Precondition:
+            This must not be recording.
         """
+        # N.B. This recording API is intended to match PyPlotVisualizer's.
+        assert not self._is_recording, "Must NOT be recording"
         self._animation = Animation(default_framerate=1./self.draw_period)
         self._recording_frame_num = 0
 
diff --git a/tutorials/rendering_multibody_plant.ipynb b/tutorials/rendering_multibody_plant.ipynb
index e57fbb450b4e..f494dbba83cb 100644
--- a/tutorials/rendering_multibody_plant.ipynb
+++ b/tutorials/rendering_multibody_plant.ipynb
@@ -434,6 +434,7 @@
    "outputs": [],
    "source": [
     "# Set the context to make the simulation valid and slightly interesting.\n",
+    "simulator.get_mutable_context().SetTime(.0)\n",
     "plant_context = plant.GetMyContextFromRoot(simulator.get_mutable_context())\n",
     "plant.get_actuation_input_port(iiwa_1).FixValue(plant_context, np.zeros((7,1)))\n",
     "plant.get_actuation_input_port(iiwa_2).FixValue(plant_context, np.zeros((7,1)))\n",
@@ -444,10 +445,10 @@
     "\n",
     "# Start recording and simulate.\n",
     "meshcat_vis.start_recording()\n",
-    "simulator.AdvanceTo(simulator.get_context().get_time() + 1.0)\n",
+    "simulator.AdvanceTo(1.0)\n",
     "\n",
-    "# Publish the recording to meshcat.\n",
-    "meshcat_vis.publish_recording()\n",
+    "# Stop recording.\n",
+    "meshcat_vis.stop_recording()\n",
     "\n",
     "# Render meshcat's current state.\n",
     "meshcat_vis.vis.render_static()"