It depends on which version you are. Xbox is behind on updates. Williams is already updated to the new liveries on PS4. Mercedes and McLaren still need to be updated.
If you seen videos of the black Mercedes it was probably a mod on F1 2019 for PC.
So no you don't have to update manually on your Xbox, you just have to wait for the patches to arrive. Williams will be soon on Xbox, the others I don't know when they will arrive.