Today is the first time I heard of this Institute, probably just like you. But apparently, it’s one of the more famous Institutes of Auckland, New Zealand.
My point being, your university alone cannot guarantee you the life you dream of. And, the reputation of the University will be based upon your achievements. Why do people think Manipal Institute of Technology is reputed? Because we all know Satya Nadella. Do you think everyone admitted there will replace him one day?
Similarly, while reviewing applications, after reading your Institute’s name, they will look at your grades. If you have good grades and work experience, they will think highly of your University (because a person of your competence chose that Institute). And the same works for mediocre grades and work experience (they will, sadly, look down upon you and the University that admitted you).
And, assuming that the reputation is not of the kind that the current students would like to hear, that will not stop you from achieving higher goals in life. A brief search in LinkedIn, and you will get to know that students from SRM have been selected for Masters in Harvard University (without any work experience after Bachelor’s Degree), and many work for Tesla (known to be quite selective as far as recruitment is concerned) now.