rst.kv

#:import Factory kivy.factory.Factory
#:import Popup kivy.uix.popup

<MyPopup@Popup>:
    BoxLayout:
        cols: 2
        RstDocument:
            id: rsttext2
        MyButton:
            text: "text changer"
            on_press: self.change_text2()


GridLayout:
    cols:2
    Button:
        text: "popup"
        on_press: Factory.MyPopup().open()
    MyButton:
        text: "text changer"
        on_press: self.change_text1()
    RstDocument:
        id:rsttext1

RST.py

from kivy.app import App
from kivy.uix.widget import Widget
from kivy.core.window import Window
from kivy.uix.button import Button
from kivy.uix.popup import Popup
from kivy.uix.rst import RstDocument


class MyButton(Button):

    def change_text1(self):
        textfield = self.parent.ids['rsttext1']
        textfield.text = "whatever"

    def change_text2(self):
        textfield = self.parent.parent.parent.parent.ids['rsttext2']
        textfield.text = "success"


class MyPopup(Popup):
    pass

class RSTApp(App):
    pass

if __name__ == '__main__':
    RSTApp().run()