So the RaMBaM put on his tefillin shel rosh on his head before his tefillin shel yad, and Josephus also says that he puts on his tefillin shel rosh first. Why did they do that? Is that even allowed today? Or is it because they are in a higher level than regular people, or did people in the olden days do that?
The premises of your question appear to be incorrect.
The Rambam (Hil. T'fillin 4:5) says to first put on the shel yad (phylacteries of the arm) and to then put on the shel rosh (phylacteries of the head):
וקושר של יד ואחר כך מניח של ראש
And he should bind the arm phylacteries [to his arm] and afterwards don the head phylacteries.
The Rambam emphasizes that a person should not reverse the order (ibid. 4:8):
שאין לובשין של ראש קודם של יד
For one should not don the head phylacteries before the arm phylacteries.
Additionally, Josephus never said to put on the shel rosh first. He simply mentioned it before he mentioned the shel yad when talking about the significance of the commandment of t'fillin in general (Antiquities iv. 8:13, "ἐπὶ τῆς κεφαλῆς καὶ τοῦ βραχίονος"). Josephus was apparently not addressing the question of the proper order of placement. English translation:
Let every one commemorate before God the benefits which he bestowed upon them at their deliverance out of the land of Egypt, and this twice every day, both when the day begins and when the hour of sleep comes on, gratitude being in its own nature a just thing, and serving not only by way of return for past, but also by way of invitation of future favors. They are also to inscribe the principal blessings they have received from God upon their doors, and show the same remembrance of them upon their arms; as also they are to bear on their forehead and their arm those wonders which declare the power of God, and his good-will towards them, that God's readiness to bless them may appear everywhere conspicuous about them.