Automatic tramssion fluid is a highly detergent oil based product. Its weight, in oil numbers is about 10 weight. In addition to making the transmission shift, it is formulated to keep the rubber seals inside the transmission soft and pilable.
One of the oldest tricks in cars is to change the oil and filter, leave it one quart low (for a five quart oil reservoir, more for a bigger reservoir), add a quart of transmission fluid and drive the car for a day or so, then change the oil and filter again. Loosens up all the gunk in the engine, and can raise the oil pressure due to more open oil passages.
In my opinion, if putting new transmission fluid in the car loosens up things that are in place because the transmission fluid is gummy enough to hold them in place, you needed to change the transmission fluid a long time ago.