Did I receive the right contact lenses?

Well, Optometrists invented contact lenses, so they are certainly qualified to prescribe them. The axis is critically important on higher diopter cylinders, but on some patients with low cylinders, it can be insignificant. Indeed, occasionally on some prescriptions the cylinder isn't even needed because the slight gap between the surface of the cornea and the inner surface of the contact lens is filled with sufficient tear fluid that the cylinder is neutralized. You also need to know that cylinder can be prescribed in a + or - direction, and the axis is rotated 180 degrees between these two prescriptions; it's just a different mathematical way to express the cylinder. Also, cylinder can shift around from prescription to prescription, particularly if you are young or a young adult, and your axis from one year might be off considerably in the next year's exam, particularly if the cylinder isn't very big. -0.75 cylinder is a modest amount of cylinder, so that is possibly what you are seeing. But the big question is, can you see well with the new prescription? If the answer is "yes," then I wouldn't be too concerned with the axis of the cylinder in such a moderate amount of cylinder as -0.75. Even if the prescription is off a little (and I don't know that it is), it couldn't cause you any damage or harm; it would just result in a little less than perfect vision. Try the lenses. If you're getting good vision, then you're probably just fine. If your visual acuity is not quite what it was with the old prescription, then you should return to the Optometrist for a follow-up refraction so he can see if your eyes are changing, or if he might have made an error in his previous refraction. Most refractions are performed automatically these days; the old days of flipping lenses back and forth in front of your eyes while shining a light in your eyes are pretty much history. The modern refractor machines do a marvelous job of prescribing a very accurate prescription for you, and they do it in seconds compared to the 20 minutes it took to do refractions the old-fashioned way.