Detail Table Won't Filter Automatically for Top N, Even When Grand Total is Correct

You need to remove the filters from the ticket id column,

Top Traveler Rank = 

VAR SelectedN = [Top N Selection Value]

VAR TravelerRank =
    RANKX(
        ALL(Travelers),
        CALCULATE([Total Amount], REMOVEFILTERS( Data[Ticket Number] )),
        ,
        DESC,
        DENSE
    )

RETURN
    TravelerRank

You'd need to do the same thing in the Is Top Traveller measure, and then add [Is Top Traveller] to the detail table as a filter, to only show when the value is 1.