Developing film is a combination of chemical processes. These processes utilize an interaction between the film and a chemical dissolved in a solution.
What do you think happens if there is too little of a chemical for the needed reaction? That's simple: the reaction stops.
Just about everything in the film developing process is based on providing the reaction more chemical than is actually needed and controlling for the reaction through time and temperature.
Development: In developing, 99% of developing is done with an abundance of developer chemical and the total development reaction controlled by temperature and time. This is why you make 1+X of your developer and develop at (usually) 20C/68F for Y minutes (whatever your developer tells you).
You need to make enough developer to cover the film, which is a function of volume. Anything extra is there for padding. What you want to avoid is streaky negatives. This can occur when there is too little developer (volume) and it runs down the partially submerged film. The film can become partially submerged through agitation when not enough fluid is used.
So, your Patterson tank says to use a minimum of 290mL - anything you add is extra padding on this. If the math works out easier to make 500mL, then do it. Keep in mind that this is using up more of your developer than necessary, but it doesn't hurt (except maybe your wallet).
Developer Exception to the Rule: When doing stand development with Rodinal, developing the chemical to exhaustion is the goal. One typically uses 1+50 or 1+100 (or even more dilution) and lets the film "soup" in it for an hour (or more). Rodinal recommends using no less than 5mL of developer (I've seen people say less. This is a highly experimental practice). But, keeping in mind that 5mL is used per 35mm roll, then your minimum volume is 500mL and you'll need to use every.last.drop to get results.
Stop Bath: I don't even measure this. Pour from the jug until the tank is full. Return to jug when done.
Fix/PermaWash: Again, the exact volume doesn't matter as the idea is that the chemical has plenty to react. Pour to cover plus a little extra to ensure proper submersion during agitation.
Photo Flow: Yep, same thing here. Although using any more than enough to cover the film is simply wasteful at this step.