We present well-resolved near-IR and sub-mm analysis of the three highly star-forming massive (> 10 11 M ) galaxies within the core of the RO-1001 galaxy group at z = 2.91. Each of them displays kpc-scale compact star-bursting cores with properties consistent with forming galaxy bulges, embedded at the center of extended, massive stellar disks. Surprisingly, the stellar disks are unambiguously both quiescent, and severely lopsided. Therefore, 'outside-in' quenching is ongoing in the three group galaxies. We propose an overall scenario in which the strong mass lopsidedness in the disks (ranging from factors of 1.6 to >3), likely generated under the effects of accreted gas and clumps, is responsible for their star-formation suppression, while funnelling gas into the nuclei and thus creating the central starbursts. The lopsided side of the disks marks the location of accretion streams impact, with additional matter components (dust and stars) detected in their close proximity directly tracing the inflow direction. The interaction with the accreted clumps, which can be regarded as minor-mergers, leads the major axes of the three galaxies to be closely aligned with the outer Lyman-α-emitting feeding filaments. These results provide the first observational evidence of the impact of cold accretion streams on the formation and evolution of the galaxies they feed. In the current phase, this is taking the form of the rapid buildup of bulges under the effects of accretion, while still preserving massive quiescent and lopsided stellar disks at least until encountering a violent major-merger.