These algea blooms are usually a result of having too many nutrients in the water for the single cell algea to feed from and multiply quickly. I agree that the water in the cup wouldnt be as green as the tank because of the lower quantity of water, but to be sure, try looking at it under the tank lights or a florecent light since different bulbs highlight different colors.
You could do a big water change and be ok for a while, but the best approach, in my opinion is to remove the food source and the algea will remove itself. Make sure you are cleaning out the gravel well, like was already pointed out, and make sure your nitrates are not getting too high between water changes. Make sure you are not over feeding at all since this will add nutrients. You may also want to look at the amount of phosphates in your water (PO4) as this can contribute as well. Many flake foods have a relatively high amount of phosphates in them as well so over feeding adds to the PO4 of your system.
A UV sterilizer would also take care of the problem for good, but I figure it is cheaper to prevent rather than buying a UV unit and bulbs for it every six months to a year.