while creating new elements of the sequence, the distribution is always "uniform"

According to that code they are randomly distributed within a cell, not uniformly distributed inside of it.

...

They need to be uniformly distributed with respect to other objects in the same cell as well as to those in neighboring cells.

BUE & Danny02: you're both using a non-probability based notion of uniform or more specifically a uniform random process. Added some text to deal with the notion of "uniform".

A group of four cells could potentially could have a greater density of flowers around their shared corner and much lower density everywhere else. The same could apply to edges with two cells. Within one cell, multiple flowers could clump together.

All these examples and opposite versions of them are likely and desirable. It's exactly what's suppose to happen. If you were to create two images with points, one globally and the other by breaking into parts and using poission and randomly choose to display one on the right and left...you shouldn't be able to identify which is which. If you can, then the hashing isn't working.

The various test-suites of PRNG quality will perform many operations in the opposite direction from this. Create a bunch of points in 'n' dimensions, then break that space up into various sized parts..count the number of contents inside each part and if the values don't approach the Poisson distribution, then it fails the test...the PRNG is not creating uniform random numbers in that number of dimensions.