The same as for the signs of any other opiate addiction. Tylox is Tylenol and Oxycodone, the principle ingredient in Oxycontin. It is highly addictive when not used as directed, and sometimes even when it is.
To answer your question, the drug is a depressant, and users seem mellow, contented and disconnected from things around them when high. When they need a fix, they are just the opposite. Until they are high again they will be emotionally volatile and irritable. They may have a runny nose, scratch as if they have a skin irritation, be preoccupied with getting out of the house (to find drugs). If withdrawal become more extreme they may have cold sweats and muscle aches and tremors, appear to be chilled.
If your person is edgy and irritable, then becomes mellow after taking the Tylox, it is very likely that he or she is addicted.