Re: Emotionally involved
IMO it means that you're mixing your personal feelings with your present situation/job.
One example I can think of comes from movies: the police negotiator during a bank heist with hostages is usually told not to get emotionally involved, that is, to not let his feelings for the hostages (especially if one of them is a relative) mix with the aim of his task: getting the attackers out of the bank, make no concessions even if they threaten to start killing the hostages...
I hope I made it more or less clear!
Please be aware that I'm neither a native English speaker nor a teacher.