My guess would be that "The general manager is doing everything he can to try to improve the team" is measured by the level of activity of the manager.
Things like total time online might be helpful, but the real improvement depends on actions - changing your squad between matches, enlarging your arena, buying new players, etc.
If this is true - it has nothing to do with actually improving the team, or how much money you have. The main thing would be your effort to improve the team, as reflected by activity.
Thus, buying and selling (since for buying you usually have to sell as well) will improve your grade here while damaging your grade in the the section:
"I am familiar with the star players, and am not afraid that they will be transferred"