Water – Should I paint wood in a roof that is not directly exposed to the outside

I'm currently in the process of replacing the roof of a room. This room was originally a balcony, so has never been part of the main house. The roof that was removed had wood beams with wood strips/planks on top of the beams, and a cement sheet on top of that.

I'm located in Bombay, India, where we get the monsoons. These are basically really, really heavy rains for a few months of the year, approx June through September. So, any roof needs to be pretty effectively waterproof. The roof described above was leaking quite badly and had some problems with mice getting in there, so had to be replaced.

When reconstructing the new ceiling, I left the wooden beams alone, and replaced the wood strips/planks. Then I put a aluminum sheet over that. On top of that goes thin strips of wood, like 1 1/2 inches vs 1 inches in width/thickness as a frame for ceiling clay tiles (I think they are clay). The tiles are quite heavy, so they just get placed into the wooden frame, not attached. Supposedly all the wood is teak, though that is hard to check. To summarize, the structure is:

ceiling tiles
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thin wooden frame for clay ceiling tiles
========================================
aluminum sheet
==============
wooden strips/planks
====================
wooden beams
============

Just to be clear, I'm not actually doing any of this; there are people doing it for me. So, I guess this is not really a suitable question for a DIY site. 🙂

My question is whether it makes sense to paint the thin wooden pieces of wood that constitute the frame for the tiles for water protection. The people who are doing it for me say it is not necessary, since the wooden tile frame won't come into direct contact with water, as the tiles are on top of it. The underlying wooden frame isn't getting painted either, but that makes more sense to me, since it is under the aluminum. However, the frame for the tiles is closer to potential water exposure.

So, does it make sense to paint wood in such a situation? More generally, how much does painting wood help to protect it from water/moisture in general?