You're right, most clinics and doctors don't test for Ureaplasma, and for good reason. It really isn't all that controversial among real STD experts. The bottom line is that all sexually active persons get Ureaplasma at one time or another; routine testing would simply pick up people carrying the organism, which rarely if ever causes disease. Therefore it isn't recommended by CDC or other STD experts and is done by few physicians in this country. Look at it as part of the normal bacteria that normal people carry. Since it's in the genitals (vagina, urethra) the organism indeed can be transmitted sexually.
That's the simple view. Things are always more complex. Newer research suggests that some Ureplasma strains may be more likely to cause real disease than others. However, no test done by routine labs distinguishes the "good" vs "bad" strains. In addition, even with the "bad" strains, actual disease has only been found in men, in whom Ureaplasma may sometimes cause nongonococcal urethritis (NGU); no important health problems are known to occur from Ureaplasma in women.
Bottom line: No real STD experts in the U.S. routinely test for Ureaplasma; and if we think it is present, no treatment is prescibed. There is some difference of opinion in different countries. For example, if you are in Spain, you're more likely to run into docs who look at Ureaplasma more seriously than I do.
With that as background, you need do nothing about your partner--indeed I fear you have done too much already, all of it unnecessary. In he gets symptoms, in particular NGU (the main symptom would be urethral discharge), he should seek treatment. Otherwise, skip the antibiotics and condoms and enjoy each other.
Good luck-- HHH, MD