Once you have signed up for Premium the "Collect Premium Prizes" button should show up on the Neopies Hubpage fairly soon after. We recommend that you go and press the button right away, so you don't risk losing any prizes. However, you technically have until the Winner of any category you voted for before becoming Premium are announced. For example, if you Voted for category 1 and then became Premium you would have until the end of the day on February 1st to press the button and get your random Premium Prize as the Winner would be announced on February 2nd.
Another Example: If you Vote for category 3,4, 5 and 6 and then become Premium you can only get categories 3 and 4's random Premium Prize until end of day February 1st, but would still be able to get categories 5 and 6's random Premium Prize until end of day February 2nd.