Saddle position/setback on a new frame

[BRad704]

I just need a mental double-check on something...

I bought a new (used) bike frame and both bikes are 73-degree seat tube angles. 2009 Fuji Team Carbon to a newer 2014 Trek Madone 4.9

I was fitted on the Fuji before, so does this mean I can take that same seatpost from the Fuji, drop it in the Madone at the proper seat height and everything will be the same?

I feel like I know the answer is YES, but the Madone feels way further back over the rear wheel...