Issue:
The gps point are in WGS84 geographic projection, after that we reproject the pts in nad83 UTM18N (Canadian and American projection) to have the coordinate in meters. After that we bring the MB back to 0:X and 0 : Y, we integrate the points in OptiSurface Designer with a txt file.

When we export the proposed design, and integrate our plan into the trimble system it opens very well into the tractor. But last week, we discovered that the field projected by the plan in the trimble system is actually slightly shifted from reality. The farther we were from our Master Benchmark, the more we seemed to be out of position. Also, the cut and fill on the existing topography is not at the right place. For example, in a field that is 1.5 km long, we were off our position by about 20 meters once at the end.

We did a topography with our system behind the tractor to see if the tractor points are shifted from our points and this is what happened. I think the points are shifted from reality and we think it's a projection problem, but we don't know for sure, and we put the MB for both files at 0 : X and 0 : Y

Answer:
The Trimble Field Level2 system with the .gps file (FMX) uses a special coordinate system where X and Y are derived from a local tangent plane with the origin at the master benchmark and elevation (Z) is derived from the geoid corrected WGS84 coordinate.
 
Using UTM coordinate system is not the same and you can end up with the design being skewed or rotated by up to 15m as you move 1km away from the master benchmark. This is a problem for Multiplane designs but even more problematic for designs with steeper slopes because a 15m horizontal error on a 1% slope can mean 150mm more soil cut or filled than required.   

There are two solutions to solve this problem:
1) Resurvey the topography with the  Trimble Field Level2 survey plugin. or
2) Transform the current coordinates you have from the coordinate system you have to the same one the Trimble Field Level2 system uses.

In future versions of OptiSurface Designer (eg V2.0) we would like to support the on the fly coordinate transformation during export but for now you can try a coordinate transformation software such as: 
Converting Latitude/Longitude to Easting/Northing