Output boosting.

Current sensing resistors at the output side of the pass transistors are used to control the regulator which drives said transistors. The idea is to attempt to keep output voltage constant under heavy load conditions, and the process should be gradual in a properly designed and adjusted supply. The fact there's a threshold which causes a jump makes me think you have a bad component somewhere in the feedback loop.

Do you have a link to the schematic for your supply?