It will not have to be refrigerated - but it should sit there and be shaken once a day for 2 weeks to a month before it's ready. It must be covered, but not ncessaril "air tight".
Could you please tell me exactly how to make it or give me a link to the place you got the instructions? I remember reading about it but I have forgotten how to get back there. I am getting some Black-Walnut s this weekend.
From what MH told me and some other people in past posts regarding that, the alcohol should keep it from spoiling or turning rancid. I would still keep it in the fridge anyway as in erring on the side of caution.