I've used several different 250mm, 350mm and 500mm mirror lenses over the years, but don't recall ever using the Tokina.
My favorite was the Tamron SP 500mm f8 (There was a Nikkor that had the same specifications and looked absolutely identical, except for a permanently installed Nikon F mount and a different design on the rubber grip of the focus ring... I suspect it was a rebadged Tamron). There were at least two versions of the Tamron SP 500mm "cat" lens.... 55B and 55BB. I don't know the differences between them or recall which I had.
That was a Tamron Adaptall2 lens, so interchangeable mounts allowed it to very easily be used on almost any 35mm camera system. I don't know about Nikon CPU vs non-CPU... but I do know Canon Tamron-EOS mounts can be bought "chipped". I've got one now on a vintage, manual focus Tamron macro lens. Cost about $40 new, including shipping from China (either via eBay or Amazon, I forget which). A lot of other mirror lenses simply use a T-mount, which also are made to fit nearly any SLR/DSLR mount, easily interchanged and available in "chipped" versions. The "chip" is supposedly programmable so that the camera will recognize the lens in a limited way (merely recording the focal length and max aperture in the EXIF). It also enables Canon's Focus Confirmation to work, which can be very helpful whenever using manual focus lenses on modern DSLRs.
I handheld the Tamron mirror lens only rarely. It was a pretty long focal length to try to do that.... plus with film I rarely used faster than ISO 200 film, more often used 100 or even 50... so was limited on shutter speeds. It had to be an exceptionally bright day to get much above 1/500 with ISO 200.
Today with the higher usable ISO on DSLRs, where much faster shutter speeds can be used, the mirror lens would be much more hand-holdable.
This was shot using a monopod (ISO 200 slide film)....
You can see the out-of-focus highlight "donuts" in the above photo... somehow they seemed less obnoxious with the Tamron lens, than some other mirror lenses I'd used.
This was shot using a tripod (also with ISO 200 slide film)...
Above photo also illustrates another of the nice features of the Tamron SP 500mm... It is extremely close focusing to about five or six feet (1.7 meters). This gives roughly 0.33X, 1:3 or one-third life-size magnification.... which is exceptional for a 500mm lens (For comparison, Canon's $9000 500mm f4 IS II focuses to 12 ft/3.7m, giving about 0.15X magnification. In fact, the highest magnification long telephoto Canon offers today is the 100-400mm Mk II, giving 0.31X. The Canon EF 300/4 lens is another close focusing tele, to about 5 feet, giving 0.24X mag.)
The Tammy 500mm was pretty darned sharp and had little distortion or vignetting. I also really liked the way it (and most other Tamron SP lenses) render colors.
The Tamron SP 500mm uses ND filters in a couple strengths to reduce light (since there is no diaphragm to "stop down"). These screw into the rear of the lens.... I think the rear filter size is 25mm or 30mm. The lens also can be fitted with 82mm in front... which is unusual for mirror lenses. It came with a set of filters (one sky, one ND, and several common color filters for B&W film). The Tamron 500mm also has a removable tripod mounting foot and came with a matching lens hood. If either of those are missing, they're hard to replace!
One of the coolest catadioptric lenses I've ever seen was the Konica Hexanon 1000mm f8... The entire mirror assembly is "fixed"... focusing is done with a small bellows at the rear. But, the neatest feature was that it had a Waterhouse Stop aperture system, where you could dial in smaller f-stops. There also was a Hexanon 2000mm f11 cat lens.... but only two copies were ever made and none were ever sold. They were huge (about 35 lbs, if memory serves) and very expensive: you could buy a modest house for the same money. (The 1000mm cost about what some cars sold for.)
I experimented using the Tamron with teleconverters, but was never very happy with any combination I tried (I had a couple 1.5X that worked very well with more standard telephotos).