Write unit tests for private method of Presenter

I'm writing unit tests for Presenters of an MVP project. My presenter implement like this:

class SplashPresenter {
    override fun onAttach() {
        if (dataManager.getAppLaunchFirstTime()) {
            onAppOpenFirstTime()
        } else {
            // Other logic...
        }
    }

    @VisibleForTesting
    fun onAppOpenFirstTime() {
        dataManager.setAppLaunchFirstTime(false)
        splashView.openLoginScreen()

        // May be I will add more functionalities in the future...
    }
}

Here we have 2 approaches to write unit test.

First approach:

Verify directly what will happen: openLoginScreen() & setAppLaunchFirstTime(false). Don't care how they will be called.

@Test
fun onAttachTest_appLaunchFirstTime() {
    Mockito.`when`(dataManager.getAppLaunchFirstTime()).thenReturn(true)

    splashPresenter.onAttach()

    verify(dataManager).setAppLaunchFirstTime(false)
    verify(splashView).openLoginScreen()
}

Second approach

We use spy() to verify private internal method onAppOpenFirstTime() will be called. Then write another separate test for onAppOpenFirstTime().

@Test
fun onAttachTest_appLaunchFirstTime() {
    `when`(dataManager.getAppLaunchFirstTime()).thenReturn(true)
    val spyPresenter = Mockito.spy(splashPresenter)

    spyPresenter.onAttach()

    verify(spyPresenter).onAppOpenFirstTime()
}

@Test
fun onAppOpenFirstTimeTest() {
    splashPresenter.onAppOpenFirstTime()

    verify(dataManager).setAppLaunchFirstTime(false)
    verify(splashView).openLoginScreen()
}

So which approach is better? Which approach will make the project more testable when extending feature in the future?

Do we need to write unit test for private internal method?