The mind-reading is implied, but not unequivocally asserted. We see him see right through her feigned powerlessness, telling her with no uncertainty that he knows she had more than enough power to deal with the problem that was at hand, then approach Tatsumaki, place his hand on her head in a reassuring-a-child-by-patting-their-head manner, assure her she has something to use her powers for, then the next panel shows a picture of her sister (as a child), and he remarks that she has a lovely sister. The sequence implies that Tatsumaki thinks of her sister when told she has something to fight for and protect other than herself, and Blast sees that mental image. This is all significantly more detailed than what we've seen of the encounter in the webcomic.
However, the nature and origins of Blast's powers are poorly detailed and highly suspicious and vast. He may have knowledge of Tatsumaki from other methods, from the mundane "dude did his research on the organization he was infiltrating/attacking" to the well-beyond-psychic.
There are implications that there is a cosmic, even Lovecraftian, entity at the works. This is implicitly the being connected to the cubes he is collecting, which we are told, by said entity, will grant any wish of power to anyone worthy. It is very ambiguously suggested that Blast may have been the recipient of such a boon, and for all we know he now has cosmic power which grants him the ability to see underlying truths of reality in a way that goes beyond simple mind reading. But then, perhaps he is not and his power has some other origin, but nevertheless may include or even go well beyond simple mind reading.