diff --git a/dvc/repo/index.py b/dvc/repo/index.py
index 32ce5b5786..ffa624df94 100644
--- a/dvc/repo/index.py
+++ b/dvc/repo/index.py
@@ -104,7 +104,7 @@ def is_out_or_ignored(root, directory):
         dirs[:] = [d for d in dirs if not is_out_or_ignored(root, d)]
 
 
-def _load_data_from_tree(index, prefix, ws, key, tree):
+def _load_data_from_tree(index, prefix, ws, key, tree, hash_name):
     from dvc_data.index import DataIndexEntry, Meta
 
     parents = set()
@@ -117,7 +117,7 @@ def _load_data_from_tree(index, prefix, ws, key, tree):
         index[(*prefix, ws, *fkey)] = DataIndexEntry(
             key=fkey,
             meta=ometa,
-            hash_info=ohi,
+            hash_info=ohi if (ohi and ohi.name == hash_name) else None,
         )
 
     for parent in parents:
@@ -151,7 +151,7 @@ def _load_data_from_outs(index, prefix, outs):
             tree = out.get_obj()
 
         if tree is not None:
-            _load_data_from_tree(index, prefix, ws, key, tree)
+            _load_data_from_tree(index, prefix, ws, key, tree, out.hash_name)
 
         entry = DataIndexEntry(
             key=key,
@@ -193,16 +193,22 @@ def _load_storage_from_import(storage_map, key, out):
         return
 
     dep = out.stage.deps[0]
-    if not out.hash_info and (
-        not dep.hash_info or dep.hash_info.name != storage_map[key].cache.odb.hash_name
-    ):
-        # partial import
+    if not out.hash_info or dep.fs.version_aware:
+        if dep.meta and dep.meta.isdir:
+            meta_token = dep.hash_info.value
+        else:
+            meta_token = tokenize(dep.meta.to_dict())
+
         fs_cache = out.repo.cache.fs_cache
         storage_map.add_cache(
             FileStorage(
                 key,
                 fs_cache.fs,
-                fs_cache.fs.join(fs_cache.path, dep.fs.protocol, tokenize(dep.fs_path)),
+                fs_cache.fs.join(
+                    fs_cache.path,
+                    dep.fs.protocol,
+                    tokenize(dep.fs_path, meta_token),
+                ),
             )
         )
 
diff --git a/dvc/testing/workspace_tests.py b/dvc/testing/workspace_tests.py
index 837d2fda0b..22232fe71e 100644
--- a/dvc/testing/workspace_tests.py
+++ b/dvc/testing/workspace_tests.py
@@ -106,6 +106,7 @@ def test_import_file(self, tmp_dir, dvc, remote_version_aware):
         (remote_version_aware / "file").write_text("modified")
         assert dvc.status().get("file.dvc") == [
             {"changed deps": {"remote://upstream/file": "update available"}},
+            {"changed outs": {"file": "not in cache"}},
         ]
         dvc.update(str(tmp_dir / "file.dvc"))
         assert (tmp_dir / "file").read_text() == "modified"
@@ -137,6 +138,7 @@ def test_import_dir(self, tmp_dir, dvc, remote_version_aware):
         (remote_version_aware / "data_dir" / "new_file").write_text("new")
         assert dvc.status().get("data_dir.dvc") == [
             {"changed deps": {"remote://upstream/data_dir": "modified"}},
+            {"changed outs": {"data_dir": "not in cache"}},
         ]
         dvc.update(str(tmp_dir / "data_dir.dvc"))
         assert (tmp_dir / "data_dir" / "subdir" / "file").read_text() == "modified"