Most companies are sensitive to the fact that your current employer is unaware you are looking. At least with cell phone and email, communication between potential employers and applicants is easy to do under the radar.
NOTE: (Company) reserves the right to contact all current and former employers for reference information.
That is standard language. They don't have to contact prior companies, but if they want to they can. Once they go beyond your current employer they will likely only get a confirmation that you worked there during those dates and that your title is approximately correct. They will not rate you as an employee, nor will they confirm projects and tasks.
Big companies will just pull your basic info from a database. Once you go back a couple of years it is unlikely that they can track down managers or coworkers anyway.
Contact my current references:
- At any time
- Only if I am a finalist candidate
Tell them only to contact your current employer if you are a finalist. And write on the application that you have not told your current management. A typical question in then interview process is why are you leaving your current job, and why did you leave previous jobs.
Why would any prospective employer request this, or what possible justification could there be?
They want to confirm that your are representing yourself accurately. Again they may not get much from your current employer beyond dates of employment and job title. Many will not want to discuss details because they don't want to be sued.
When they use the term "finialist" they mean they will offer you a job if the references checkout. You may or may not want to accept based on the offer details, but they are ready to hire you.
How should one proceed when confronted with this situation?
Check the box to have them contact your current employer if you are "finalist". For most or all of the previews ones check "at any time".
If you are switching, your company will eventually find out. Start thinking about what you will tell them.
EDIT: The question was asked by the OP in the comments:
Is it considered unethical to look for another job without letting the current employer know? Or is there the sense that one should not try to hide the fact from the current employer?
It is not unethical to look without telling your boss. In the United States most people can quit at anytime. They don't have a contract, so they have no obligations. You don't have to tell until you want to tell. You can get an offer one day and tell the boss as soon as you sign the offer. Most give 2 weeks notice, but there is no requirement.
Should you hide the fact your are looking?
Perception is everything. Some people are concerned that if their employer knows they are looking they will get fired. Some employers think that if anybody was insane enough to look anywhere else they deserve to be fired. Thankfully both of these examples are in the minority.
You don't tell too early because you never know how long the process will take. It can take weeks or months from application submission to start date, even if you are the perfect candidate.
Once you tell them you are looking they will start to treat you differently. They will not include you in their long term plans. they will not send you to a training class, because you will be gone soon. Forget about them wanting to put you on the cool new project. Most will not fire you though. Some will help you in your search. The smart ones will start looking for a replacement.