hydro-repellent treatment is recommended for tubs used in wet climates like Singapore, Hong Kong etc.

About the mold: you should provide a good natural ventilation (open doors or windows after the tub). Forced ventilation alone, will not be enough.
In any case, we treat the tubs with a hydro-repellent product (see here).
http://www.bartokdesign.com/japan/downloads/kihadaichiban-description.pdf
"KIHADA ICHIBAN" is applied by brush or roller. It does not create a coat, it actually penetrates inside offering lasting protection whithout occluding the pores of wood.

Hinoki wood is generally unfinished to convey its soft touch and natural aroma. Anyway, this new product (based on the nano-technology and using a fluoride base) operates like the silicates treatments used in europe to waterproof bricks or plaster.
These products penetrate inside the material so they do not leave a peel, they do not alter the color, luminosity and aroma of the wood.

We have been using this product for 4 years now.
It is great to prevent mold and we did not have any claim from Singapore customers so far.