According to you the property is in the name of your sister and her (deceased) husband.
Your sister's husband has died without leaving any WILL.
Therefore his 50% share in the property will go by way of inheritence equally to all his Class-I heirs i.e. his widow (your sister) and the 2 minor sons.
There is nothing automatic.
Your Sister has to approach the Tehasildar/SDM's office under whose jurisdiction they are living and apply for grant of Legal Heir Certificate. (This certificate is necessary in connection with the immovable property).
If any bank balance, FD, or insusrance etc., has been left behind by your sister's husband, the same can be realised if anybody has been registered as a NOMINEE. After the nominee gets the money, the same has to be shared between your sister and her two minor children.
In case there is no nomination, and succession certificate is required by the authorities for release of the amount, then for obtaining the succession certificate (it is for the movable properties like bank balance, FD, insurance etc.) by approaching the District Court.
Now coming to the house property. There are two options:
1. After obtaining the Legal heir certificate she can approach the Municipal Authorities for making mutation entries based on the legal heir certificate.
2. After having obtained the Legal heir certificate simply keep quiet, as the original documents of the property + legal heir certificate will put together will demonstrate that your sister and her two sons are the owners of the property.
Pl. note, during the minority of her two sons, your sister will not be able to dispose of the property. In case she wants to dispose of the minor's share in the property, then she has to approach the District Court and obtain necessary permission for sale of the minor's property.