Do user-specific tags automatically apply to new devices when a user registers them?

It depends on how the tag was created, not on an account setting.

When you create a tag in Pushwoosh you choose its scope:

• General (default, user_specific: false) — the value is stored per device (HWID). Each device of the same user holds its own value independently, and a newly registered device starts with no value. General tags do not propagate to new devices.
• User-specific (user_specific: true) — the value is stored per User ID. Setting it via the User ID applies it to all of that user's devices at once, and any new device that registers with the same User ID inherits the value automatically.

So: user-specific tags do automatically apply to new devices of the same user; General (device-scoped) tags do not.

Conditions for automatic application:

• The tag must have been created as user-specific. Scope is chosen at tag creation and applies from then on.
• The new device must register with the exact same User ID.

If a tag was created as General and you need cross-device behaviour, either re-create it as user-specific, or push the value to every HWID of the user with /setTags.

Example of setting a user-specific tag via User ID:

{
  "request": {
    "application": "XXXXX-XXXXX",
    "userId": "the id of a specific user",
    "tags": { "subscription_tier": "premium", "loyalty_points": 350 }
  }
}

If a tag really is user-specific, the User ID matches, and values still do not appear on the new device, contact our support team.