I played around with this a few years ago. I tried several calls, and had some success with both the Hoochie Mama call, and even better with the "It Maka Da Bull Crazy" call. A few times with the latter call had some incredible responses with bringing herds literally RUNNING across a pasture for about 800 yards to within a few yards.
However, the success was short-lived. It appears, from my experience, that axis learn pretty quickly and once they figure out it is someone with a call, they won't respond at all after that. So for the past year or so, the calls have stayed in the bag mostly.
Ironically, the best responses and use I have now is simulating a doe alarm call or chirp. While bucks often ignore a bugle, it has been my experience that they respond well to a doe exhibiting distress - especially during the rut. But don't over do it. One or two calls is enough for a buck to respond - if he is going to respond at all. Young bucks seem to respond more. And does will often be curious if they hear an alarm call - at least to the point where they want to see where it is coming from - before bolting off.
So far as drawing in bucks from distance - very limited success. In hunting situations, I now limit the use of calls to only attempting to (a) "reposition" the animal, or (b) attempting to stop an animal that is already on their way departing. In these cases is where I have more success.
For example, I see some axis but they are too far away for a shot, or are holding tight/deep within the brush offering no shot. A single chirp can sometimes cause the animals to take a step or two out of the brush to identify the source, or alter their path a few steps towards you to see what is going on. Again, a rutting buck seem to be very protective of does - and if they believe a doe is in distress, they will come to see what is going on.
Sometimes it's just that little bit that help present a shot.
But so far as bringing in bucks looking for a fight, similar to whitetail - really haven't had that happen but once or twice. Axis bucks are much more cautious - and the times I believe they respond, they don't come "charging in" - but simply stroll a little closer.
The only exception I ever saw to this was one of the very first times I was using the call. After a hunt, I was standing with my daughter's BF near a fence line, looking at a group of axis about 800 yards away in the neighbor's pasture. There was a fence on our side, a road, and a fence on the other side of the road - then the axis off in the distance. I said, "let's see if those animals respond to the call". We were standing, in the open, right next to the fence. A tooted a couple of times, and all the axis looked up. Then a group of 6-8 younger bucks came charging toward us at full gallop. We were shocked, and froze on the spot. This group of bucks stopped about 30 yards on the other side of the fence. One of the small bucks walked right up to the fence and began to bark at us not 30 feet away.
We "talked" back and forth for about 10 full minutes. He was getting very aggressive and I really thought he was going to jump the fence at come after us. Then they simply walked off. I tried giving a few more chirps and that one buck barked at us over his shoulder as he walked off. LOL
I have tried the calls at other ranches, with other herds. All I can say is that typically you can get some sort of response the FIRST time you use the call. Then they wise up and don't ever respond - even months later. So keep that in mind.