Use custom intent action to launch activity only in specific application context

I need to specify my login activity with intent filter:

    <activity
        android:name=".view.LoginActivity"
        android:label="@string/app_name">
        <intent-filter>
            <action android:name="com.example.sdk.LOGIN" />
            <category android:name="android.intent.category.DEFAULT" />
        </intent-filter>
    </activity>

The reason why I want to do it that way is that I am developing an SDK that I want to use in few projects and this is the best way I could figure out of how to notify the SDK which is the login activity, while it is defined only in the app module.

After I do such declaration I start the login activity like so (both in library and app):

    Intent intent = new Intent();
    intent.setAction("com.example.sdk.LOGIN");
    context.startActivity(intent);

There is the possibility that two or more applications relying on the same SDK will be installed simultaneously on the same device. If I get it correctly, in such case in each of these applications the Activity start will launch a random login activity (with the possibility of the call in application A launching the login of application B).

1. Am I correct in my understanding of how custom intent filters work?
2. Is there a way to tell the call in application A to use only intent filter declarations in application A

Suggestions of alternative approaches to reusing the login-related logic, not relying on intent filters are also welcome.

I figured out a way to achieve what I wanted.

Basically I do not hard code the package in my library, rather I start the login activity from the library using:

private static final String INTENT_ACTION_PATTERN = "%s.LOGIN";
public void startLoginActivity() {
    Intent intent = new Intent();
    String intentAction = String.format(INTENT_ACTION_PATTERN, mContext.getPackageName());
    intent.setAction(intentAction);
    mContext.startActivity(intent);
}

And I will just use a convention that I will always define the custom intent filter to match the package of my application:

<activity
    android:name=".view.LoginActivity"
    android:label="@string/app_name">
    <intent-filter>
        <action android:name="com.example.myapp.LOGIN" />
        <category android:name="android.intent.category.DEFAULT" />
    </intent-filter>
</activity>