"There are ten birds on top of the car right now."
That would be "Ten birds are now on top of the car", but ideally you would still add a 有 before the 十只鸟.
现在十只鸟在一辆车上。 Two problems I have with this sentence. The first is that the alternate sentence isn't marked correctly and secondly they assume that car means auto (汽车)，it could be any car like a train car for example, so the more general word "车” should be used without the “汽”。Furthermore it could be argued that the general “车” would be understood to mean car if used in a sentence.
The phrase is (在)汽车上in the same way as it’s (在)书包里 or (在)桌子下。It’s just the way that mandarin puts it.
There might be other phrases that use 上 first E.g. 他有三本以上的书籍 or somewhere else: 椅子的下面
but (在)。。。上is how this one works.