I am not a plumber or a PRO.
I don't know why it would make the noises during certain times of the day ... I have never heard of that before. Maybe some of the plumbers on this blog will have come across it before.
A few thoughts:
- Does it make the noise when you walk around it? That might be easier to replicate for the builder.
- If not, maybe you can record it for them.
- It does not look like they screwed the tile flange to the studs. Do the instructions for that tub call for that?
- Why did they cut out the drywall above the tub? Looks like it was done after the fact. Did they notice and try to fix this issue?
- John Gayewski has indicated the tub does not look like it is appropriately supported. This is beyond my expertise, but I would raise it with your builder.