I was wondering about settlement myself - then I ran some quick numbers to see if it was possible without having to do extraordinary things like pile driving, drilling caissons, etc..
If on rock - good. On good bearing soil (like sands or gravel) - good. If on soil with predominantly silts or clays... then I personally would consult a geotechnical engineer to estimate the settlement and give recommendations. I'm guessing by the magnitude of the tank, his engineers would have done the homework and consulted a geotechnical engineer if he wasn't comfortable with the soil conditions.
For those reading this thread - I'll explain some of the numbers I came up with: With a tank that is 8 ft tall tank you're looking at 500 lb/square foot of pressure (8ft * 62.4lb/ft^3 = 499.2 psf - assuming evenly distributed) just due to water. This should be well within the limits of soils for their bearing capacity. However, it can still produce settlement - from negligible (bedrock) to constantly settling (soil with lots of organics).
Now what he's doing is not unheard of - people build indoor pools all the time - even on the upper levels of hotels. Just takes a little planning and he appears to be doing it. There are very likely public aquariums probably built with less thought than what's going on with this build.
It stinks when people - with good intentions but not the technical acumen - second guess the work going on. However, asking questions so you can learn more about the project and offer advice is what this forum is all about.