diff --git a/tests/integ/scala/test_function_suite.py b/tests/integ/scala/test_function_suite.py
index 6c4404b4606..ce9244c7091 100644
--- a/tests/integ/scala/test_function_suite.py
+++ b/tests/integ/scala/test_function_suite.py
@@ -1833,6 +1833,19 @@ def test_to_timestamp_numeric_scale_column(
     ],
 )
 def test_to_timestamp_variant_column(to_type, expected, session, local_testing_mode):
+    data = [
+        12345678900,  # integer
+        "12345678900",  # string containing integer
+        "2024-02-01 12:34:56.789000",  # timestamp str
+        datetime(2017, 12, 24, 12, 55, 59, 123456),  # timestamp
+    ]
+
+    if to_type == to_timestamp_ntz and IS_IN_STORED_PROC:
+        # integer in variant type depends on local time zone of the server
+        # while in sproc reg test, the timezone is non-deterministic leading to non-deterministic result
+        # here we pop the case of integer in variant type
+        expected.pop(0)
+        data.pop(0)
     with parameter_override(
         session,
         "timezone",
@@ -1842,12 +1855,6 @@ def test_to_timestamp_variant_column(to_type, expected, session, local_testing_m
         # as we are testing Variant + Integer case
         # this timezone has to be the same as the one in session
         LocalTimezone.set_local_timezone(pytz.timezone("Etc/GMT+8"))
-        data = [
-            12345678900,  # integer
-            "12345678900",  # string containing integer
-            "2024-02-01 12:34:56.789000",  # timestamp str
-            datetime(2017, 12, 24, 12, 55, 59, 123456),  # timestamp
-        ]
         df = session.create_dataframe(
             data,
             StructType(
diff --git a/tests/integ/test_df_to_pandas.py b/tests/integ/test_df_to_pandas.py
index d33e79a0ec9..3f31909a6bf 100644
--- a/tests/integ/test_df_to_pandas.py
+++ b/tests/integ/test_df_to_pandas.py
@@ -265,7 +265,9 @@ def test_to_pandas_batches(session, local_testing_mode):
         break
 
 
-@pytest.mark.localtest
+@pytest.mark.skipif(
+    IS_IN_STORED_PROC, reason="SNOW-1362480, backend optimization in different reg env"
+)
 def test_df_to_pandas_df(session):
     df = session.create_dataframe(
         [
@@ -365,15 +367,23 @@ def test_df_to_pandas_df(session):
             "A": pd.Series(["[\n  1,\n  2,\n  3,\n  4\n]"], dtype=object),
             "B": pd.Series([b"123"], dtype=object),
             "C": pd.Series([True], dtype=bool),
-            "D": pd.Series([1], dtype=np.int64),
+            "D": pd.Series(
+                [1], dtype=np.int64
+            ),  # in reg env, there can be backend optimization resulting in np.int8
             "E": pd.Series([datetime.date(year=2023, month=10, day=30)], dtype=object),
             "F": pd.Series([decimal.Decimal(1)], dtype=np.int64),
             "G": pd.Series([1.23], dtype=np.float64),
             "H": pd.Series([1.23], dtype=np.float64),
-            "I": pd.Series([100], dtype=np.int64),
-            "J": pd.Series([100], dtype=np.int64),
+            "I": pd.Series(
+                [100], dtype=np.int64
+            ),  # in reg env, there can be backend optimization resulting in np.int8
+            "J": pd.Series(
+                [100], dtype=np.int64
+            ),  # in reg env, there can be backend optimization resulting in np.int8
             "K": pd.Series([None], dtype=object),
-            "L": pd.Series([100], dtype=np.int64),
+            "L": pd.Series(
+                [100], dtype=np.int64
+            ),  # in reg env, there can be backend optimization resulting in np.int8
             "M": pd.Series(["abc"], dtype=object),
             "N": pd.Series(
                 [datetime.datetime(2023, 10, 30, 12, 12, 12)], dtype="datetime64[ns]"
diff --git a/tests/integ/test_function.py b/tests/integ/test_function.py
index dc1b76cc474..7d6e088c7a5 100644
--- a/tests/integ/test_function.py
+++ b/tests/integ/test_function.py
@@ -163,6 +163,8 @@
     StringType,
     StructField,
     StructType,
+    TimestampTimeZone,
+    TimestampType,
     VariantType,
 )
 from tests.utils import TestData, Utils
@@ -388,13 +390,15 @@ def test_date_or_time_to_char(session, convert_func):
             datetime.datetime(2021, 12, 21, 9, 12, 56),
             datetime.datetime(1969, 1, 1, 1, 1, 1),
         ],
-        schema=["a"],
+        schema=StructType([StructField("a", TimestampType(TimestampTimeZone.NTZ))]),
     )
     assert df.select(convert_func(col("a"), "mm-dd-yyyy mi:ss:hh24")).collect() == [
         Row("12-21-2021 12:56:09"),
         Row("01-01-1969 01:01:01"),
     ]
-    assert df.select(convert_func(col("a"))).collect() == [
+    # we explicitly set format here because in some test env the default output format is changed
+    # leading to different result
+    assert df.select(convert_func(col("a"), "yyyy-mm-dd hh24:mi:ss.FF3")).collect() == [
         Row("2021-12-21 09:12:56.000"),
         Row("1969-01-01 01:01:01.000"),
     ]