Orange Oil is an environmentally friendly alternative to traditional methods of exterminating termites. I recommend calling several agencies, doing cyber research, and then getting recommendations. There are many "green" termite exterminators that you can hire who will do a great job and watch out for the environment.
Educating the public about the dangers associated with some common pests, will help people understand the danger that termites, rodents and cockroaches (to name a few) pose to their home, their family and local pest control services staff.
Although it is not considered mainstream yet, and many don't consider orange oil to be a do-all, end-all termite treatment, it is certainly worthy of consideration as a least-toxic termite management option.
My first thought would be, who is telling you it is supposed to be "better than traditional tenting"? I ask this question because I know that there is much discussion and controversy about this method, which would make me wonder that if it's all that great, why is there controversy? If it was so good, then why would it not catch on right away and become a real staple in the industry? I personally cannot comment on any experience as all my clients have ultimately chosen to go the traditional path, even when the company they chose can do both methods. You may want to check with the pest control board to obtain some additional information: http://www.pestboard.ca.gov/index.shtml.
One item to check closely when you do go forward is check the company's warranty information - when and under what circumstances will the company come back without charge to retreat. That should help protect yourself and may offer a clue into what methods the industry may stand behind.
Is it better for the environment? Yes. But does eradicate termites as well as the traditional tenting? Not exactly. I've had clients start with orange oil, just to get it tented within the year. There is something to be said for tenting and having good woodwork done on the property. I know a couple of great termite companies that I could suggest if you want the work done well and in a timely manner (and I can imagine that as a landlord, those are two of your biggest concerns).
Each method has it's positives, personally I like that is is a natural chemical which is known and safe. With any method you use you will need to followup and retreat as needed. If it kills the termites when used it has done it's job!