Lower Bounds for the Set Disjointness Problem
That's simply a different problem.  The set disjointness problem is defined, by common agreement, to be the problem where the universe has size $n$ and the inputs (sets) are represented as a bitvector of length $n$.  In other words, when you hear the phrase "set disjointness problem", you can know that's what they're referring to, and not the problem you care about.

It's fair to ask about the communication complexity of your problem.  I don't know what its communication complexity is.  There is no reason to assume your problem will necessarily have the same complexity as the set disjointness problem.

(There's a natural randomized protocol for your problem: if Alice and Bob each have a set of $n$ 64-bit integers randomly pick a universal hash function $f$ from the space of 64-bit integers to the set $\{1,2,\dots,2n\}$, transmit a description of $f$, hash the elements, and check disjointness of the hashed elements.  If there is a common element among the hashes, use binary search to find all common elements and check if the unhashed elements match as well.  The expected communication cost is $\Theta(n)$.  It's also clear that any algorithm must have communication complexity $\Omega(n)$.  This still leaves open what is the communication complexity for deterministic protocols, or the worst-case communication complexity for randomized protocols.)