(Fake) Spy wills: does the order of visits matter? Example:

Real spy writes: n1 - B:(10) | MV(player1/player2/player3)

Fake spy writes: n2 - B:(10) | MV(player2/player3/player1)

I guess I hadn’t thought this mattered in the past, but 3 games I’ve had recently, in low diamond, have had lynches based on the order of the names written. 

I guess I always thought a spy could write the names in any order. Same as a fake spy (specifically mafia fake spy), no matter what order the names are put on screen. So I never used this in my personal decision making factor, too many variables in my head.

Am I wrong here? Should I put more weight into the order of the names? 