Basically I am trying to understand the public opinion about why the Tamil Tigers are regarded as so notoriously evil while the Sri Lankan government isn't blamed.
It looks like the Tamil Tigers were formed due to the increasing pressure put on by the Sri Lankan government to suppress Tamil culture. This included language, traditions, the burning of the Jaffna library and all around discrimination and ethnic cleansing. The government seemed to be just as ruthless as the LTTE in their indiscriminate killing of civilians in the Tamil areas.
Why then is the LTTE one of the worst terrorist organizations of all time while the deeds of the Sri Lankan government that instigated their formation and fuelled their grievances not publically condemned?
Hi, I wrote an in depth look at the issues of the Tamils in Srī Lankā here. It is fairly long so you may want to start with part 6 which leads up to the independence movement.
But to further answer your question, international agencies DO put a lot of blame on the Srī Lankan government for the Civil War, especially the authoritarian conservative that dominated between 1970 and 1977, when they were finally overthrown. The more liberal government attempted to balance the demands of Sinhalese nationalists with minorities (though mainly appealing to Sinhalese moderates) and implemented half-hearted reforms that failed to properly address Tamil demands nor to quell the separatist movements.
Their tepid response to the burning of the Jaffna library and the 1981 riots only sped up the process of radicalizing young Tamils. Certainly, their responses to Tamil violence were disproportionate.
But I'm worried you are whitewashing the LTTE here. As brutal as the Srī Lankan government was, the LTTE were far worse. While you cite indiscriminate killing of civilians in Tamil areas by the Srī Lankan government, it did happen, but it wasn't a part of the strategy like it was for the LTTE, nor was it nearly as prevelant. I'm bashing my head against the 20-year rule here, but the LTTE were pioneers in modern terrorism, redefining how child soldiers, suicide bombers, fear tactics, and other insurgence techniques were utilized to control and create fear in a populace. They participated in ethnic cleansing of their own and their end goal was the creation of an independent ethnostate.
So it's less that the Srī Lankan government was "good" (they weren't, they were corrupt and fractured at best, and brutally repressive at worst), but the LTTE were much worse. A more extreme version would be the Assad forces versus ISIL.