Universal aspects of the critical Casimir force f_c in wetting films of ³He-⁴He mixtures near their bulk tricritical point are studied within models of the corresponding universality class. f_c for such films of thickness L is calculated along isotherms at several fixed concentrations of ³He. Nonsymmetric boundary conditions impose nontrivial concentration profiles leading to repulsive force which exhibit a rich crossover behavior between the tricritical point and the line of critical points. The theoretical results agree semiquantitatively with published experimental data and emphasize the importance of logarithmic corrections. The universal Casimir amplitude is the amplitude of the leading behavior ~L^-3(ln L)^1/2 dominating the contribution ~L^-3 whose amplitude is nonuniversal and which is comparable with the background dispersion force contributions.