Most likely your issue is coming from the type of stain you used; which we haven't found out yet.
Based on your description, it sounds like you are using an oil based stain. Oil based stains (like Minwax) are known for having bleed out due to using a cheaper oil like linseed oil. And since red oak does have larger pores, the stain will pool during application and slowly bleed out as it dries. This does not mean you will get a bad finish. You will just have to wipe off any excess oil and wait for it to dry completely.
Not to get too technical, but the color in the stain comes from tiny, tiny balls of the pigments that are suspended in a fluid medium; oils, water, etc. When you wipe the stain "on" the surface, you are forcing these balls of pigment "into" the pores. As the stain dries, the fluid medium evaporates and leaves the pigment behind.
Red oak is a fine choice for aquarium stands; mine is built from red oak (and with an oil based stain).
One recommendation I would have made prior to finishing the stand would have been to sand up to a 150grit/180grit finish at a minimum. Sanding only to a 120grit finish is still very course when it comes to finishing wood projects; especially oak. Using a conditioning medium will help fill those pores for a more even finish.
I have seen way too many nice projects get "ruined" by a bad finish because people do not take enough time to sand the wood to a very fine finish. The wood should feel like glass prior to staining as the moisture from the stain is only going to cause the grain to swell; albeit minimally.
I've had great success using red oak and oil based stains over many years, but I know that there could be some bleed out; not every time, but I'm aware it could happen.
Your stand will be fine.
Good job and good luck!