This is a very broad question and no one except the respondents in question know exactly what they believe and why.
However, I suspect one important result in this context is the Second Welfare Theorem.
In simple language and subject to some assumptions:
The First Welfare Theorem tells us that any competitive equilibrium leads to a Pareto efficient allocation of resources.
The Second Welfare Theorem tells us that almost any Pareto optimal equilibrium can be achieved via the competitive mechanism, provided appropriate lump-sum taxes and transfers are imposed on individuals and firms.
The main idea here is that markets lead to efficiency. Thus, no intervention of the government is required. However, a situation where someone holds every good and the rest of the population holds none, is also a Pareto efficient distribution. This distribution can hardly be considered as perfect under any welfare definition. The second theorem helps us here.
The two main issues economists are concerned about in this context are efficiency and distribution. The first is all about not wasting resources and maximizing the total economic pie. The second issue is about distributing that pie. The first theorem tells us that a free market achieves an efficient allocation. The second tells us that we can achieve any distribution we want through transfers without harming efficiency.
It is unlikely that the one particular efficient allocation which results from a free market (out of the endless possibilities) also is optimal from a distributional point of view (and optimal distribution will depend on a society's preferences). Luckily, according to the Second Theorem, we can use transfers to achieve both optimal efficiency and distribution. Hence, it is unsurprising that many economists would be in favor of that.
The controversies start with discussion how exactly to design those transfers. Any economist would agree that lump sum taxes and distribution are optimal. However, these taxes are considered impossible politically, which means we often have to rely on transfer mechanisms that trade-off efficiency and distribution.
About your question "is there substantial evidence showing that the policy of governmental redistribution improves absolute well-being of poor people?": The answer must be yes by definition. If we give poor people more resources it can be safe to assume that their economic well-being is improved.
