diff --git a/homeassistant/helpers/debounce.py b/homeassistant/helpers/debounce.py
index 2fe42e19a67..773fff6ebc6 100644
--- a/homeassistant/helpers/debounce.py
+++ b/homeassistant/helpers/debounce.py
@@ -109,7 +109,7 @@ class Debouncer(Generic[_R_co]):
 
             assert self._job is not None
             try:
-                if task := self.hass.async_run_hass_job(self._job):
+                if task := self.hass.async_run_hass_job(self._job, eager_start=True):
                     await task
             finally:
                 self._schedule_timer()
@@ -130,7 +130,7 @@ class Debouncer(Generic[_R_co]):
                 return
 
             try:
-                if task := self.hass.async_run_hass_job(self._job):
+                if task := self.hass.async_run_hass_job(self._job, eager_start=True):
                     await task
             except Exception:  # pylint: disable=broad-except
                 self.logger.exception("Unexpected exception from %s", self.function)
diff --git a/tests/components/bluetooth/test_active_update_processor.py b/tests/components/bluetooth/test_active_update_processor.py
index 13045048fc1..e894ef3dab4 100644
--- a/tests/components/bluetooth/test_active_update_processor.py
+++ b/tests/components/bluetooth/test_active_update_processor.py
@@ -330,7 +330,7 @@ async def test_second_poll_needed(
     inject_bluetooth_service_info(hass, GENERIC_BLUETOOTH_SERVICE_INFO_2)
 
     await hass.async_block_till_done()
-    assert async_handle_update.mock_calls[-1] == call({"testdata": 1})
+    assert async_handle_update.mock_calls[1] == call({"testdata": 1})
 
     cancel()
 
diff --git a/tests/components/hue/test_light_v1.py b/tests/components/hue/test_light_v1.py
index fc2163326bb..9a74d9cd994 100644
--- a/tests/components/hue/test_light_v1.py
+++ b/tests/components/hue/test_light_v1.py
@@ -413,6 +413,8 @@ async def test_group_removed(hass: HomeAssistant, mock_bridge_v1) -> None:
     await hass.services.async_call(
         "light", "turn_on", {"entity_id": "light.group_1"}, blocking=True
     )
+    # Wait for the group to be updated
+    await hass.async_block_till_done()
 
     # 2x group update, 1x light update, 1 turn on request
     assert len(mock_bridge_v1.mock_requests) == 4
@@ -440,6 +442,8 @@ async def test_light_removed(hass: HomeAssistant, mock_bridge_v1) -> None:
     await hass.services.async_call(
         "light", "turn_on", {"entity_id": "light.hue_lamp_1"}, blocking=True
     )
+    # Wait for the light to be updated
+    await hass.async_block_till_done()
 
     # 2x light update, 1 group update, 1 turn on request
     assert len(mock_bridge_v1.mock_requests) == 4
diff --git a/tests/components/shelly/test_config_flow.py b/tests/components/shelly/test_config_flow.py
index 7ce111fdf21..c3c1fc36c2e 100644
--- a/tests/components/shelly/test_config_flow.py
+++ b/tests/components/shelly/test_config_flow.py
@@ -1,6 +1,7 @@
 """Test the Shelly config flow."""
 
 from dataclasses import replace
+from datetime import timedelta
 from ipaddress import ip_address
 from typing import Any
 from unittest.mock import AsyncMock, Mock, patch
@@ -21,13 +22,15 @@ from homeassistant.components.shelly.const import (
     DOMAIN,
     BLEScannerMode,
 )
+from homeassistant.components.shelly.coordinator import ENTRY_RELOAD_COOLDOWN
 from homeassistant.config_entries import SOURCE_REAUTH
 from homeassistant.core import HomeAssistant
 from homeassistant.setup import async_setup_component
+from homeassistant.util import dt as dt_util
 
 from . import init_integration
 
-from tests.common import MockConfigEntry
+from tests.common import MockConfigEntry, async_fire_time_changed
 from tests.typing import WebSocketGenerator
 
 DISCOVERY_INFO = zeroconf.ZeroconfServiceInfo(
@@ -1030,6 +1033,9 @@ async def test_zeroconf_already_configured_triggers_refresh_mac_in_name(
 
     monkeypatch.setattr(mock_rpc_device, "connected", False)
     mock_rpc_device.mock_disconnected()
+    async_fire_time_changed(
+        hass, dt_util.utcnow() + timedelta(seconds=ENTRY_RELOAD_COOLDOWN)
+    )
     await hass.async_block_till_done()
     assert len(mock_rpc_device.initialize.mock_calls) == 2
 
@@ -1062,6 +1068,9 @@ async def test_zeroconf_already_configured_triggers_refresh(
 
     monkeypatch.setattr(mock_rpc_device, "connected", False)
     mock_rpc_device.mock_disconnected()
+    async_fire_time_changed(
+        hass, dt_util.utcnow() + timedelta(seconds=ENTRY_RELOAD_COOLDOWN)
+    )
     await hass.async_block_till_done()
     assert len(mock_rpc_device.initialize.mock_calls) == 2
 
@@ -1100,6 +1109,9 @@ async def test_zeroconf_sleeping_device_not_triggers_refresh(
 
     monkeypatch.setattr(mock_rpc_device, "connected", False)
     mock_rpc_device.mock_disconnected()
+    async_fire_time_changed(
+        hass, dt_util.utcnow() + timedelta(seconds=ENTRY_RELOAD_COOLDOWN)
+    )
     await hass.async_block_till_done()
     assert len(mock_rpc_device.initialize.mock_calls) == 0
     assert "device did not update" not in caplog.text