I am not sure if there is a time period but would guess anything within a week would be acceptable. I have not traded in but have ordered a phone from them when I began and it is shipped next day(business day) by FedEx. I would think if you ordered it the week before Christmas with the holidays I don't think it would hurt to send it after the Xmas holiday.
Just to point out if you buy a phone on your account from Visible it will be locked for 60 days. I have read that it has to be used on your account and not a different account for that time period before it is unlocked. So if you are giving it as a gift for someone on Visible it will work but the phone will never unlock. If you are giving it to someone on a different carrier the phone may not work. If it is an iPhone you might be better off trading it in to Apple instead and get an unlocked phone. Android phones are hit or miss on being compatible if ordered outside of Visible, Pixels are known to pass for the most part, Samsung is about a 50% chance and Motorola needs to be bought from Visible to pass compatibility.
Hope this helps.
