Access to better schools is a factor in selecting a locality within the city but I don't think it has been a deciding factor in deciding the city itself.

Many cities including tier-2 cities have a variation of one of those "international" schools that parents seek and there's no significant difference in the quality of education between them.

Apart from the usual cycle of available talent + job opportunities, Bangalore has better weather and location wise it can attract talent from 4 states(these 4 states are major contributors to IT workforce compared to other states) while not being too far from place of origin.

better schools is not a factor at all. right out of college, or a little later most of the high quality engineers move to Bangalore because that's where the jobs already are. once people settle down a bit, they tend to be averse to move on average. it's network effect and sheer inertia. no one really wants it this way.