Yes, the courts should oversee elections because candidates and other stakeholders have been known to use fraud, intimidation, and other criminal means to force a result that is favorable to them. By keeping a close eye on such activities, the courts can make sure that elections truly reflect the will of the people rather than the will of those with both the power and the willingness to subvert the democratic process.
The three branches of government in any democracy have a responsibility to the public to keep a system of checks and balances in place. If the courts review the results of a referendum and determine that something illegal has occurred, then they are doing their part to ensure the purity of the election of executive branch officials.
Regarding Austria's presidential election result being overturned, courts should only serve an important role of overseeing the election. Courts should have no rule and overturning the will of the people unless there is a legally binding reason to do so. Courts have a one function - to interpret the law and that is all. It should not make law.
I believe that the roles and duties of the judiciary should keep it far away from politics. This is especially the case when members of the courts and the judiciary are, on the whole, unelected officials. To think otherwise is, in my opinion, to compromise democracy and expose the judiciary to undue pressures.