updateTag updates unrelated tags

Link to the code that reproduces this issue

https://github.com/prananta/next-use-cache-private-bug

To Reproduce

1. npm run build
2. npm run start
3. open localhost:3000
4. click one of the Refresh buttons

Current vs. Expected behavior

According to the doc in https://nextjs.org/docs/app/api-reference/functions/updateTag, updateTag is supposed to update cached data for a specific cache tag. But in my repo, updating certain tag updates other cached data with different tags too. In the repo example, i have three functions that use use cache, use cache: remote and use cache: private respectively. They also have different tags.

export const timeInAsia = async () => {
  "use cache: remote";
  cacheTag("time-in-asia");
  cacheLife("hours");
  console.log(`Fetching Asia time`);
  await new Promise((resolve) => setTimeout(resolve, 1000));
  const now = getDateInTimezone("Asia/Tokyo");

  return now;
};

export const timeInUTC = async () => {
  "use cache";
  cacheTag("time-in-utc");
  cacheLife("hours");
  console.log(`Fetching UTC time`);

  await new Promise((resolve) => setTimeout(resolve, 1000));
  const now = getDateInTimezone("UTC");

  return now;
};

export const timeInAmerica = async () => {
  "use cache: private";
  cacheTag("time-in-america");
  cacheLife("hours");
  console.log(`Fetching America time`);

  await new Promise((resolve) => setTimeout(resolve, 1000));

  const cookieStore = await cookies();
  console.log(cookieStore.getAll());

  const now = getDateInTimezone("America/New_York");

  return now;
};

When I called updateTag('time-in-utc') from a server action for example, not only timeInUtc is re-executed, but also timeInAmerica. The updateTag's behavior is unpredictable right now. Sometimes it only updates the cached data for given tag, sometimes it affects other tags too. This happens in both dev and production.

Provide environment information

Operating System:
  Platform: darwin
  Arch: