RAW failed in saving Sheikh Mujib because by that time (1974) they were overconfident.
Rakkhi Bahini was a RAW invention and used RAW advisers as an army raised exclusively as personal army of the Sheikh, to save him and bolster his one party rule organization (BaKSAL). Rakkhi Bahini's uniforms even were ditto copies of that of the Indian Army. To say that the Bangladesh Army command was enraged - was an understatement.
Rakkhi Bahini - in the name of "curb(ing) the insurgency and maintain law and order - became involved in numerous charges of human rights abuse including political killings,[3][4][5] shooting by death squads,[6] and rape.[5] It was seen as the armed wing of the ruling Awami League[1] and it swore an oath of loyalty to Sheikh Mujibur Rahman.[7]
The army sore allegiance to the Sheikh himself, and not the country, Bangladesh.
en.wikipedia.org
One country, one party, one army to back it all up. RAW formed this army exclusively to suppress opposition and kill activists of opponent parties like BNP, Jamaat and other parties. So yes - India is responsible. This is all very well-documented.
Rakkhi Bahini was disbanded as soon as the Sheikh's entire cohorts were put to death. Again - another failure of RAW in history, just like the one last year.