Why is du command showing double size when h flag is sent?

The size on OSX (which I assume you have from the computer name) is calculated on 512-byte blocks because the BSD version of du is used (other versions, like the Cygwin's one I am using now on Windows, behave differently).

So for every 1K you get two blocks, apparently doubling the value of every size.

They're both correct. In the second case, the unit is blocks (512B each). 1 kilobyte = 2 blocks.