Hi Kim,
MiniZinc doesn't have explicit interval variables. Intervals are generally represented using two integer variables (start time + duration or start + end time). With newer versions of MiniZinc you can actually create tuples or records to represent intervals.
In communication to the solver these variables are not necessarily connected, but I would assume that solvers like IBM CPOptimizer can reconstruct these variables when used in scheduling global constraint, such as disjunctive or cummulative.
Cheers,
Jip