Being Indian car maker and our affinity for foreign products, it will be very difficult for them to shed that image. Even these days, I have met people who still associate Tata = trucks.
I agree that people associate Tata Motors with trucks, though I would not see this as an Indian vs foreign thing. Mahindra, for example, though being an Indian brands sells good numbers of XUV500, and Boleros.
Similarly in two wheelers, though Honda is the market leader, Bajaj and TVS are still doing good business and are well trusted.
If it had been just affinity for foreign products, GM. Ford, VW and Skoda would have thrived. however that is not the case.
We also have Japanese brands like Nissan (though just a brand name here), who haven't been successful in the market.
We have to accept that not everyone looks for the same thing. For many car buyers, the car is just an instrument to take them from point A to B in good comfort.
Safety(unfortunate), fun to drive, and brand experience does not count for them. As long as the car holds its value, costs less to maintain and gives a fuss free experience, that's all that counts.
Hyundai and Maruti precisely understand this and are offering the same. Toyota is a brand built with reliability in mind. This is the reason they under tune their engines, so that they can give more reliability without stressing the engines much.
People don't buy Toyotas looking at their power figures, or feature lists. They purchase it with the trust the Toyota logo has built.
Tata Tiago has now been accepted and Nexon also is seeing a much better response as compared to earlier. Tata is re-building its brand and we need to be patient and wait for the change in public perception.