The battens should be cut to the inside of the "water bar".
The valley is made from GRP (Glass Reinforced Plastic). As you can see on the photos, just underneath the edge of the tiles (where the battens end), you can see where the GRP valley looks a different colour, and rough-looking - this is a sanded strip which is where the mortar grips onto the valley, and beds the tiles on.
It is most definitely NOT finished, all the cuts need removing, battens cutting back, and tiles bedding on using a strong 3:1 mortar mix (on the sanded strip, as the mortar won't grip straight to the plastic.
If the valley doesn't guide the rain water into the gutter then he needs to put a lead saddle at the bottom of the valley, (under the valley and into the gutter). Which should be fixed with clout nails or screws (obviously under the tiles, before they are bedded on).
And as you mentioned, them cuts are fairly bad lol.
If it's left like that then your friend is right - the battens will soak up water and rot, and if you get high winds then there's the risk of water going up and over the water bars into the roof space. Also, the cut tiles, or even full tiles can be blown off, even when clipped.