I am not a native of Karnataka, and therefore probably do not have the right to make any remark on this issue.
However, on the basis of common sense I feel that the Tulu language should be made the second official language of Karnataka. The state has sizeable Tulu speakers, mainly concentrated in the districts of Udupi and Dakshina Kannada. And one key town of the state where the language has a prominent number of speakers is Mangalore. In a nutshell, the Tulu language does have a strong position in Karnataka. And therefore that position must be duly recognized by giving it the second official language status in the state.
The step will also help the Tuluva people in carving out a separate identity for themselves, in a stark contrast to the present situation where they are often confused with the Kannadigas. And this in turn will also stimulate the thriving and nourishment of the Tuluva culture (which includes the famous Udupi cuisine), which is right now probably a bit overwhelmed by the Kannadiga culture.