That's the ASSUMPTION that DEFINES the CMIF simultaneity method. But it is not true in the Dolby&Gull method, or in the Minguizzi method, or in my method (which I'm going the christen as "the Fontenot method"). That was the reason for it being called a paradox. People thought that the traveler SHOULD be able to use the time dilation equation for the entire trip, because they thought that surely that one instant of acceleration couldn't make a difference. But we know that SOMETHING has to make a difference, because they have to agree about who's older when they are reunited (because they are standing right there looking at each other). He may conclude she is ageing more slowly than he is during some parts of the trip, but he DOES find her to be the older at the reunion, so she HAS to be ageing faster than him SOMETIME during the trip (according to him AND to her).