Looks like you started out with a DS1820 example, since the DS18B20 doesn't have COUNT_REMAIN and COUNT_PER_C registers.

To answer your original question, yes it does normally default to 12-bit.
However, any resolution can be stored in non-volitile memory, in which case it will power-up at that reolution instead.

But with any resolution, the calculation is the same ( * 625, DIV32 10).

Bruce's page I pointed to previously covers that, and more.

Hope it works out for you.
<br>