Our livers dump whenever it detects our levels are low. We all know this.
In normal healthy people hormones trigger the pancreas to secrete insulin to regulate the dumped glucose and also tells the liver to stop dumping.
In T2 diabetics with insulin resistance this system breaks down. The liver dumps, the pancreas secretes, but the insulin doesn't work properly because it is resisted by the liver cells. The glucose levels remain high and the liver continues dumping, the pancreas panics and secretes more and more insulin until enough is produced to stop the liver dumping more glucose and push the glucose into the cells for energy/storage.
(I have no knowledge about pumps or injected insulin, but imagine that if there is insulin resistance then this artificial insulin will also be rejected and will need extra in order to regulate the dumped glucose and stop the liver from dumping more.) Maybe insulin/pump users can help more with this.