As a Sikh who wears a turban as a part of my religion, should I have safety concerns or take precautions in order to travel to Turkey? Are there other things I need to think about while being there, as an Indian Sikh?
99.8% of the population identified as Muslim, according to wikipedia, so your turban won't be a problem anywhere in Turkey, especially in Izmir. It is one of the most modern city in Turkey and people are really respectful in there no matter what religion you have and what you wear.
You should not concern about this.
In your case, I don't think there will be any problem. The Turkish neither know much about the Sikhs nor they care about them, to be honest. So even if you went to the most religious and intolerant parts of the Turkey -I come from one of those parts- I would doubt that you would encounter any reaction.
However, going to any place in Turkey with a clothing that made a serious statement for Christianity or against Islam would not be the wisest choice. Especially these days secularism and tolerance to other cultures are not the most cherished principles. Though even in that case, I would not think anything more serious than nasty looks and verbal attack is likely in general.