One of the core guiding principles in 5e is that the specific overrules the general:
This book contains rules, especially in parts 2 and 3, that govern how the game plays. That said, many racial traits, class features, spells, magic items, monster abilities, and other game elements break the general rules in some way, creating an exception to how the rest of the game works. Remember this: If a specific rule contradicts a general rule, the specific rule wins.
To understand how to resolve this, it is important to understand the basic rules so you can see which parts are being changes.
Normally when you are reduced to 0 hp, you are knocked unconscious:
When you drop to 0 hit points, you either die outright or fall unconscious, as explained in the following sections.
When damage reduces you to 0 hit points and there is damage remaining, you die if the remaining damage equals or exceeds your hit point maximum.
If damage reduces you to 0 hit points and fails to kill you, you fall unconscious.
Whenever you start your turn with 0 hit points, you must make a special saving throw, called a death saving throw, to determine whether you creep closer to death or hang onto life.
On your third [failed death save], you die.
How do Juiblex and the Nightwalker modify these rules?
We can see that Juiblex is an exception to this rule, it "dies only if it starts its turn with 0 hit points and doesn't regenerate." This means that Juiblex will survive any number of failed death saves, so long as they can regenerate.
The Nightwalker also overrides some of these rules. Usually when a creature is reduced to 0 hp it is unconscious, unless it suffers instant death, and then it has to fail 3 death saves to die. However when reduced to "0 hit points from damage dealt by the nightwalker dies and can't be revived by any means short of a wish spell."
So what happens if Juiblex is reduced to 0 hp by a Nightwalker?
Well, Juiblex modifies the instant death and saving throws part of the rules. But the Nightwalker modifies what happens when you are reduced to 0 hit points.
The key point is that the Nightwalker's ability makes something die. Normally something that dies, becomes dead. However, Juiblex has a special ability that modifies this expectation. In this case, Juiblex's ability modifies the general rule, so Juiblex survives.