Measurements of mass and angular distributions of fission fragments from actinide nuclei 249Bk and 257Md, produced in fusion reactions 11B and 19F + 238U, are presented. Experimentally observed mass ratio distributions indicate “multi-chance fission” through the interplay of fission modes in the fission process, and they agree well with predictions from calculations using the GEF (“GEneral description of Fission observables”) model code. Furthermore, to test the signatures of events from non-compound nuclear processes in the fission of 249Bk and 257Md nuclei, Monte Carlo statistical decay model calculations using GEMINI++ were performed for the measured mass distribution at all energies. For comparison purposes, the fission fragment mass distributions of neighboring heavy actinide nuclei, previously measured in the fission of 250Cf and 254Fm nuclei produced by 12C and 16O projectiles on a 238U target, are also presented. The measured angular anisotropy data for the 19F + 238U reaction differ from the results of the Transition State Model (TSM) at energies below the fusion barrier. As a result of the present study, we suggest considering the interplay between K relaxation time, dynamic dissipation, and their influence on shell correction to understand the evolution of fission dynamics in heavy-ion-induced actinide nuclei.