You automatically get one, but it only counts for the effect, not for participation. For instance, at 3p, if you build without participating and only 1 other player participates, the edifice is a failure and you just get protection from the penalty (which can be useless or important it depends). If you participate and you are the only one, you wasted the gold cost because you are still just protected. If successful, though, indeed it's double reward. That's part of why Ur day is stronger : you are free to choose a token that is very likely to be useful (tipycally the third one but not always) and you control the outcome more. Ur night is sometimes good but it's extremely rare and hard to use even then. It kind of needs cooperation from some players which is hard to anticipate and risky to bet on. I strongly suggest Ur day in almost every case, and most of the time go red.
The Ur effect is much clearer IRL because the special Ur token is actually taken from the box (independantly from the decision to participate) and not from the card. That's why BGA Ur is so confusing : it seems to appear out of thin air and it can be hard to compute how it counts.