The main point would not be the source of the money but the decision process.
Let's imagine that we have some kind of magic oracle that can tell us the utility of each $ used for each project1. Then the government should be expected to spend the money in order to get the most utility of it.
If your governor wants to build a road and that road has a high utility/cost2 ratio, then providing additional funding only helps to increase that ratio (as the cost will be lower); it was ethical to build the road without contributions and it would be ethical to build it with contributions.
If that road has a not so high utility/cost ratio but with the additional funds its increased ratio makes it worthwhile, it would be ethical to build it.
If even with the donation that road has a low utility/cost ratio, then the money should go to better projects.
And as always, conflicts of interest should be averted. If the governor wants to build a road that happens to connect his factories to the port (thus giving him a vested interested in its construction), that conflict of interest should be made public and evaluated3 to avoid any impropiety or even the appareance of impropiety. Then again, that the governor is supplying part of the money is not essential to this point.
And one issue with development programs that must be taken into account is how sustainable it is. If a road is built this year thanks to the governor funds... there will be enough funds to maintain it properly if the governor stops providing his own money the next year? Again this could be a problem even if the money was not from a third party, but in this case the fixation of the governor with getting his plan executed could lead to these issues further down the road.
1Of course in real life, ideological differences can make agreements about "utility" very difficult: someone will think that building road to improve economy gives the most utility, others will claim that education needs more funds, others than the first priority should be healthcare...
2Cost for the state.
3A private company paying for some public works that will benefit it is not unheard of, and hardly unethical if the end result benefits the country. The issue here is to ensure that the decision is taken for the benefit of the country and not of the decision maker.