Who was Urahara before the exile?

He was the Captain of Squad 12 and the founding president of the Shinigami Research and Development Institute — a position that suited his intellectual temperament precisely. He built the institute into one of Soul Society's primary knowledge-generating institutions.

He was appointed Captain young and was not a comfortable fit institutionally. His interest was knowledge and its applications, not politics or hierarchy. He respected the institution to the extent it served genuine purposes, and was skeptical of it where it did not.

What happened with the Visoreds?

A group of Captains and Lieutenants — including Shinji Hirako, Love, Rose, and others — had been subjected to Hollowfication experiments. Urahara discovered this and attempted to reverse it. He partially succeeded — they survived — but the process could not undo the Hollow nature that had been forced on them.

He was accused of conducting these experiments himself. Aizen, who was actually responsible, had perfectly positioned Urahara to take the blame. Rather than fight an institutional process that had already decided his guilt, Urahara accepted exile and used the opportunity to work outside the system.

How does this history affect his relationship with the Visoreds?

It is complicated. He saved their lives but could not restore them fully. Some of them held this against him for years. The relationship is not warm, but it is honest — they know what he is and what he did and did not do, without the full picture for most of the series.

His acceptance of responsibility for something he did not do, in service of a longer game he believed necessary, is consistent with his character: willing to be wrong in the short term to be right in the outcome.