Can an eye doctor detect an orbital tumor with a basic eye exam? or is that the job of an ophthalmologist? possible to notice tumor w/o certain tools?

Usually not: Refering to an eye doctor you mean optometrist. He checks eyes with regard to focusing and the nature of the lens to employ in glasses. The ophthalmologist examines the eye with an optholmoscope looking at the ontent of the globe and the retina and as to how the rectus muscles focus the eye. An orbital tumor can be seen or suspected based on appearance of retina and when needed MRI ordered