With in this sense just indicates that something happened (more or less) at the same time as something else, but it does not indicate a cause / effect relationship.
In the case of your deer, the development of the elongated metatarsals did not, in itself, cause some fingers to become hooves (hooves are at the end of the limb, metatarsals are in the “middle” of the hand or foot. The two things happened (more or less) simultaneously and can be seen as related development.
One reason to use with here is to actually avoid the impression that evolution is result of “moving towards a goal”; the only causes are mutation and natural selection. An animal does not develop hooves because its metatarsals elongate.
In the second sentence, there seems to be a semantic cause / effect relation. It is likely that the staff working overtime did actually at least partially cause the project's timely completion. However, the sentence does not actually explicitly indicate that the overtime caused that timely completion!
It is even feasible to interpret the sentence the other way around: because we were working to finish the project on time, the staff was working overtime.
The only thing the sentence claims is that the project was completed on time, and in the process of doing that, the staff was doing overtime. Whether the reader wants to see that as a compliment to the staff (because of your commitment we finished on time!) or a remark about the project management (your deadlines caused the staff to work overtime) is up to the reader. Such ambiguity may or may not be a conscious intent of the author.
In many cases, people consciously or subconsciously use these kind of wording to avoid making “hard” statement they can be held accountable for. If you explicitly say the project finished on time because the staff worked overtime, it can mean that you imply overtime is needed to finish a project on time. It can also be interpreted as a comment about project management not having contributed to the success. By simply noting that two things happened (project finished on time, staff did overtime) you leave it to the reader to come to a conclusion.