Kotlin code
Use ActionMode.Callback to finish ActionMode after menu item pressed
 private val actionModeCallbacks = object : ActionMode.Callback {
    override fun onCreateActionMode(mode: ActionMode, menu: Menu): Boolean {
        mode.menuInflater.inflate(R.menu.menu_action_mode, menu)
        return true
    }
    override fun onPrepareActionMode(mode: ActionMode, menu: Menu): Boolean {
        return false
    }
    override fun onActionItemClicked(mode: ActionMode, item: MenuItem): Boolean {
        when (item.itemId) {
            R.id.menu_item -> {
                mode.finish() // after click of menu item close action mode
                return true
            }
        }
        return false
    }
    override fun onDestroyActionMode(mode: ActionMode) {
    }
}
startSupportActionMode
(activity as AppCompatActivity).startSupportActionMode(actionModeCallbacks)