The perception of mental weakness comes from 3 places imo.
1) The real emotional nature of DC's smack talk in the fights.
2) The rep he had in wrestling.
3) The fact that we watched him mentally break in the last two rounds, throwing out his whole striking strategy vainly attempting to get a takedown just to prove he could do it. And all this only to find out the guy he fought barely trained and was doing blow not long before they fought. DC must honestly know real fear of what clean, hard training Jones can do. Jones has B-level wrestling credentials and DC could barely get his arms around him. If you've wrestled at the Olympic level, that's severely mentally damaging.
Jones has physically broken plenty of fighters, but no one has been mentally dominated the way DC has, except maybe Rashad who was psyched out for other reasons.
(1) and (2) are pretty weak evidence. As for (1), fighters get emotional all the time in press conferences, interviews, and so on. It may be that during these moments there is weakness, but there is no justification in them for broad-scale inferences regarding their mental states. Plenty of angry fighters have gone on to win their fights. It just doesn't mean enough.
Regarding (2), his rep was that he got very emotional, not that he was mentally weak. He reached the highest levels of wrestling for Christ's sake. Olympics and World Championships. 6 of his 10 collegiate losses were to Cael Sanderson, possibly the greatest college wrestler ever.
(3) I find full of assumptions. How do you know that he was "vainly attempting to get a takedown just to prove he could do it"? Do you think that once he got it, that he wanted Jones to get right up? Clearly he thought his best shot to win the fight was to get Jones down at all costs at that point. Again, this is something that's happened in a million fights, and we don't call the fighters in question mentally weak.
The charge sounds like trivial psychologizing, and it's guesswork at best. The same kind of thinking is applied constantly to fighters at weigh-ins ("He's SHOOK"), during walkouts ("He looks mentally defeated"), and basically every interview that's sparked with any emotion.
It's pretty much GSP all over again. He's seeing a sport's psychologist---that's mentally weak! Look how careful he fights now---he's scared! Etc. The reverse applies too---"Just look at Conor's confidence! He's mentally defeated Nate."
Jones is the better fighter---that's by far the most important fact here. But psychology is easier to talk about than techniques and strategies.