Delayed γ-ray cascades, originating from the decay of (6⁺) isomeric states, in the very neutron-rich, semimagic isotopes (136,138)Sn have been observed following the projectile fission of a ²³⁸U beam at RIBF, RIKEN. The wave functions of these isomeric states are proposed to be predominantly a fully aligned pair of f(7/2) neutrons. Shell-model calculations, performed using a realistic effective interaction, reproduce well the energies of the excited states of these nuclei and the measured transition rates, with the exception of the B(E2;6⁺→4⁺) rate of ¹³⁶Sn, which deviates from a simple seniority scheme. Empirically reducing the νf(7/2)(2) orbit matrix elements produces a 4₁⁺ state with almost equal seniority 2 and 4 components, correctly reproducing the experimental B(E2;6⁺→4⁺) rate of ¹³⁶Sn. These data provide a key benchmark for shell-model interactions far from stability.