Agitation is useful as a control, like time and temperature. It has a direct influence on grain in that it can reduce highlight densities that were grossly over exposed, or, over agitated. Rodinal grain is finer with 3 or 5 minute rest cycles than with constant agitation. Time was, you could see a difference between 30 second and 60 second intervals with Tri X, but not so anymore. While the primary link to fine grain is the use of a low pH developer, like Xtol or Microdol-X, relative grain is increased by too much exposure or over development. Minimal agitation reduces relative grain.
You've got 3 problems. The first is that you MUST agitate the film.
The term 'standing development' is misunderstood today. Of course you have to agitate the film, primarily to make the density even across the film. With 120, and with real Rodinal, agitation cycles of 3 to 5 minutes are safe, but that depends on the film, and the reels, and the tank. (Goodness knows what paRodinal does.) With 35mm, you can usually rest the film for up to 10 minutes. The thing is, you gain all the benefits by resting the film for 5 minutes, and there is really nothing to be gained by resting for longer times. There is BIG difference between agitating every minute, and agitation every fifth minute. There is a lot of room for fine tuning your film.
Secondly, you need to fill the tank with developer first, then load the reel. Pouring the developer in and out is often a cause for uneven development. I'm just assuming you poured the developer in after closing the tank.
Third, when you agitate, agitate. Move the developer around.
My first teachers learned their craft in the early 1900s, and were proponents of what they called 'standing development'.
What they taught me in the 1960s, however, was what we call today 'minimal agitation.