Are you using any form of particle caching in Maya?
The Krakatoa Partitioning requires the particles to be “free agents” during the simulation.
It has two different approaches to randomization.
If the distribution is fully procedural (based on a random seed), then varying the random seed option would be the simplest approach. By incrementing the random seed, each partition will seed particles elsewhere throughout the emitter, producing a unique initial pattern which will affect all future frames.
If you are using an Initial State that enforces the positions of all particles on the first frame only, then using the random jittering of the position and/or velocity lets you somewhat vary the initial positions taken from the Initial State data. However, on all later frames after the first, the particles should be free to move according to the fields and other factors defined in the simulation. The randomization of positions and velocities is performed only on new-born particles, which explains why you see a difference on the first frame only.
However, if you have an active Maya Particle Cache applied to the simulation, the positions of all particles will be fully determined by it, and we won’t be able to vary the future behavior of the particles after they are born - we let the simulation run without modifying it beyond the first frame, and if the cache is resetting the positions and velocities to the stored data, we cannot do anything about it.
A workaround would be to use the Repopulation operator to seed completely new particles around the single set of cached base particles, but the looks would be very different from what you would get with correct partitioning, so I don’t recommend it in this case.
In short, if you have a cache on your system, turn it off - the saving of PRT partitions is technically a form of caching anyway. It will be slower, but should produce what you expect. If you are not using a cache and you are still not getting the right behavior, we might need to see a simple test scene to reproduce the problem as you might have encountered some bug we are not aware of…