While answer by SubChord is correct, is doesnt really answer the question of how to set the "on" color without also affecting other widgets. To do this, use a ThemeOverlay
in styles.xml:
<style name="ToggleSwitchTheme" parent="ThemeOverlay.AppCompat.Light">
<item name="colorAccent">@color/green_bright</item>
</style>
And reference it in your switch:
<android.support.v7.widget.SwitchCompat
android:theme="@style/ToggleSwitchTheme" ... />
In so doing it will ONLY affect the color of the views you want to apply it to.