I don't know about direct payments for publishing, but one often hears the phrase "publish or perish," with regard to university faculty positions, and I long ago (long, long ago, as a student) ran into a negative impact from this: professors who could not care less about doing a good job teaching, and apparently unhappy, in at least one of those cases, to be required to teach. I suppose that often, publishing is by far the most important issue to a university professor.
Quite the opposite for me, during my career with the US federal government, largely with a statistical agency producing Official Statistics on the energy industry, publishing was not required at all. In fact, management very much appeared to consider it was doing an employee a favor to even pay a publication fee or to send you to a conference, and I paid some fees myself, and did much of my publication work, and virtually all referee work, outside of business hours. In one case, a leading, internationally renowned statistician told me that I was the world's leading expert in a certain area, and that I should write a paper on it. I did, but it took me a year, doing it all on my own time, because my supervisor said he did not want me working on it. This, in spite of the fact that it was key to solving huge problems at work, and after I wrote it, I included it in training for new statisticians that came to that statistical agency, and worked in the unofficial team that I was allowed to run. Further note that I put this article in a less formal, online only journal, as I did a great deal other work, to document methodologies in the spare time that I found. So you can see that publication of any kind was not a priority, though I think it was arguably quite important.
In 2011 I was invited to publish an article in a special issue of the Pakistan Journal of Statistics (PJS), in honor of Ken Brewer. I read where there was, I think, about a $500 publication fee. My office refused to pay it. I then determined to pay it out of my own pocket, but the PJS editor kindly told me that since I was invited, I would not have to pay the fee.
Later, at work, I was told that it was a 'non-monetary' award for me, that a hardcopy of the PJS journal issue sent to me, that contained my article, was on display on a coffee table.
So, you can imagine my reaction when I saw this question, asking if one's institution might have paid a reward for publishing. You asked about universities and institutions. I assumed you were not limiting this to educational institutions. For the problem solving research and development that I did, including implementation to provide many important results, there seemed to sometimes be random punishments, but to pay a fee to someone for publishing a paper was certainly never considered. The very idea might garner a huge laugh.
I have no such information in India where money is paid for publishing in ISI or other listed journals. But there is ta practice calculating individuals Performance Indicator by giving prefixed scores tp published papers for the purpose of promotion fresh recruitment