To me it depends a bit on the actual illness. Since covid and the common cold have similar symptoms, I'd probably tell him right away. But in normal times, if you take the flu for example, I don't think most people would change their behavior if they knew they had contact with somebody who has it now (even though there's probably some spread before the infection really shows), nor do I think that you could even tell who gave it to you in the end. I try not to bother my T all the time with texts, and that information would probably be superfluous to him. On the other hand, if it were any illness which is dangerous and or highly transmissible, I'd tell him. Like if I developed tuberculosis, probably good to tell him, just like when you figure out you have an STD and had sexual contact with somebody just a bit prior...