3 simple questions:
Is Dalai trying to separate Tibet from China?
Is that harmful to China?
Is India supporting Dalai?
I dont mean to be rude but the Dalais principle supporter is not India but the USA and European Powers. If you read into history the safeguard on Dalai was by USA before he moved to India - yet the primary focus is (only) India by you. Yes he is in India but if you start counting the number of dissidents, asylum seekers, separatists (according to PRC) from PRC to other countries you will be surprised that India is not the no.1.
There is far more activity by those people that is much more harmful to PRC compared to what Dalai is doing. Also those people are trying to do to PRC that is much worse compared to what you perceive in Tibet. Also India has given refugee to Dalai because of traditional links and location and takes no position on Tibet independence and self-determination.
Also leading back to main point where are the most dissidents - separatists (according to PRC) of the PRC located. Will you arm that countries neighbor(s) to try and destabilize with nuclear weapons and also financially bank-roll and support their army when they have no money basically create distress. Even worse support that neighbor that has a policy of supporting terrorism.
Talk about double-standards !!
Please note that the above is a little off-topic and what happened was really sad and terrible. Condolences and it would be good if the PRC leaders are able to identify the main cause and source of this terrible thing. I am sure India will support PRC on the endeavor. It is also a cause of concern this has happened in areas where there was no such history.