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 solving a longstanding open problem (only decidability was known so far). By-product results with other concrete domains and other logics, such as description logics with concrete domains, are also briefly presented.