Hi, not correct. A mini-lab printer DOES adjust for every frame.
Early mini-lab machines typically had three color sensors somewhere after the negative, so they could measure the average amount of light (and color) coming through the negative. They would change both the exposure time and the filtration in an attempt to get a roughly grey average. This is similar to the way we use a light meter to measure exposure for an outdoor scene, and the earlier mini-labs were easily fooled in the same ways. If you took photos outdoors in the snow, the mini-lab printer would want to print it too dark; it was up to the operator to notice this possible problem, and override the machine by pressing the appropriate density or color buttons.
Different types of film had different characteristics, so the machines were pre-calibrated for specific film types. This was done with the assistance of printer setup negatives (often called "Shirleys") which were available on different films. The results were saved on a "channel," and it was always necessary to select the proper channel for the customer's film type.
Printing errors due to "non-average" negatives was an ongoing problem with such printers until Agfa came out with their "MSC" mini-lab, incorporating the first (to my knowledge) built in scanner. Although the scanner was low resolution, it was the first time such machines could be "smart" about the scene content, and adjust accordingly. They were a bit like today's advanced "matrix metering" cameras, compared to an averaging meter.