From the conclusion at the end: "... mental fatigue limits exercise tolerance in humans through higher perception of effort ..."
So, according to them, it's the perception that changes with mental fatigue, not because there is any physiological reason to be tired.
When you exercise, the increase in cortisol results in a 50% increase in endurance compared to if there was no cortisol increase, at least in rat experiments [1].
Given that cortisol is involved in both mental alertness and physical endurance, it seems like it could be a plausible reason for this finding.
1. https://www.researchgate.net/profile/Mehis_Viru/publication/...