NO.
Jello Pudding Mix does not contain any milk so if you're allergic to milk you can still make and eat Jello Pudding.
You can also use Almond Milk, Soy Milk etc to make Jello Pudding Mix if you're allergic to regular cows milk and the Jello Pudding mix will turn out just fine.
I have made Jello Pudding Mix using both Almond Milk and Soy Milk before and the Jello Pudding turned out just fine.
When you do make the Jello Pudding though most people use regular cows milk so if the Jello Pudding is already made and you're allergic to milk then you should not eat the Jello Pudding unless you know what type of milk it was made from.
I've also made Jello Pudding Milk with water but using milk is much better for a more thicker Jello Pudding.