What exactly was Tatsuya afraid that Mizuki could discover with her sensitive eyes?
If my understanding was correct, he was afraid that she would discover his unique constitution (the extremely high psion count he had) which allowed him to use some of his really overpowered and rarely seen spells such as Gram Demolition. Knowing that he has this specific constitution would make him a suspect when spells that require this constitution are cast.

Tatsuya tried (and failed miserably) to keep a low profile and avoid divulging any information about his powers, as some of these were national secrets (due to him being a special member of the JSDF 101 Independent Magic-Equipped Battalion) and the Yotsuba wanted his and Miyuki's identity as members of the family to remain secret.