We introduce the class of tree constraint automata with data values in ℤ (equipped with the less than relation and equality predicates to constants), and we show that the nonemptiness problem is EXPTIME-complete. Using an automata-based approach, we establish that the satisfiability problem for CTL(ℤ) (CTL with constraints in ℤ) is EXPTIME-complete, and the satisfiability problem for CTL*(ℤ) is 2ExpTime-complete (only decidability was known so far). By-product results with other concrete domains and other logics, are also briefly discussed.