On the change date, the fare valid on the start date of the trip will be applied to the entire itinerary. (The booking class and seasonality of each flight will apply to the outbound and return flight boarding dates.)
A Flex round trip is purchased on 5/25, with an outbound part (7/1, ANA 253, Tokyo/Haneda to Fukuoka) and an inbound part (10/3, ANA 258, Fukuoka to Tokyo/Haneda).
If changes are made to the reserved flights for the outbound (7/3, ANA 253, Tokyo/Haneda to Fukuoka) and inbound (10/4, ANA 258, Fukuoka to Tokyo/Haneda) parts on 7/1, the fare amounts valid for the start date of the trip on the day that the changes are made (= 7/1) will be applied for both parts.