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.
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