You are a serial killer, a psychopath (as the question asks what the word (singular) is). You have a particular pattern of killing (for example, with a specific weapon, people with specific profile, location etc.). Now, another person saw you doing the above. The person doesn't match your profile. So, out of your domain of killing, you are watching (i.e. the person doesn't match your killing profile and hence he is out of your domain (pattern) and also, killing is your domain but you are just watching here) that person. You are really angry at that person as you see (with anxiety) where your train (your chain of killing would go; i.e. as an SK, you want to set a record of kills etc.). So you zoom forth on that person (focus on that person) refraining now because you haven't clearly planned how to execute that person (as it may leave a clue and you don't want to get caught). But you still watch that person's every move.
Additionally,
Also, I see you sounds the same as Icy you and ICU where in the former, you caught that person (as you exclaimed I see you (as in you got the right moment)) and froze him to escape blood evidence and in the latter, you just injured him severely to admit him in ICU