Answering to add more to Jerry's answer, so start your reading there.
Stand development is a technique of developer exhaustion - you use very little developer chemical and leave it to "do its thing" for about an hour. It's quite possible the development is actually exhausted before, but that 60min is a tried and true amount of time.
So, time matters little and more time won't lead to over development. So what does? Amounts!
It is not enough to say that you'll use Rodinal at 1:100 ratio. If you use 2mL of Rodinal and 200mL of water, you may not have enough actual developer chemical to develop the role to completion before exhaustion occurs. This will lead to underdeveloped negatives.
Adox puts it on the bottle that their recommendation is to use, at minimum, 5mL of Rodinal per roll of 135/120.
If you search online, you'll find stories of people using as little as 3.5mL per roll. Stand Development is more art than science in this regard - many people attempt many different things and you'll need to experiment to find what you like.
Now, how does this affect pushing the film in development? Pushing in dev is the process of overdeveloping a negative to compensate for underexposure. But, how can you overdevelop if you are developing to exhaustion? The only way is to include more actual developer.
I've played around with it some and have settled up on using an extra 1mL per stop pushed. So, if I shot Ilford FP4 (stock ISO 125) at ISO 250, then I'd develop in 6mL of Rodinal at 1:100. Shot at 500: 7mL Rodinal at 1:100.
Conceptually, I hope this makes sense. In practice, it's very, very experimental. What you find working for one film may produce garbage in another. But, the first step is to find a baseline amount of Rodinal to use in stand developing film shot at or below box speed, and then experiment with a single film and that same amount of Rodinal and additional amounts...keep it up until you find something you like and don't forget to write it down!