In my opinion...put a 4' or 6' level on that damp area and see what the deviation is. I'm not sure how long after it rained that that picture was taken, but it appears only to be damp...so maybe the "dip" or the low spots aren't that bad. if there were puddles..that's a different story...the dips/low spots might be a but deeper. In my mind, and I think the general rule of thumb is, a level slab is desired to keep the water level in the tub level. I don't think shimming may be the best option to fix a low spot in the concrete. If the low spot is "that bad", and that area is going to be concealed by the tub, have your guy apply a latex modifed cementitious repair mortar (such as SikaTop 123+ or something similar) to level it off.
Nick B
Middleton, Ma