No service needed. I'm speaking about the specific condition of bright daytime backlight. In the shade/overcast, or when the sun is low, no problem. Purple everywhere, otherwise. While fringing may be a problem for a lot of fast lenses, it is not true of all. Specifically the lenses with Canon's BR element: EF 35mm f/1.4L II, and the RF 85mm f/1.2L.
I'm not entirely clear if it's CA at the plane of focus or bokeh CA that's the issue. With that said...
Since I tend to shoot this lens at night or in less contrasty situations (i.e. indoors) I just walked outside to try and recreate this. Power line against blue sky had virtually no CA at the plane of focus. Power line against a bright white cloud (full sun illuminating at an angle to the cloud) had some. But I've seen worse from other lenses in less stressful conditions, and it was easily corrected in PS.
Bokeh fringing is certainly there in all lighting conditions, but this is true for nearly every fast lens. Even the few lenses which correct for it, like the two you mention, still show it to some degree. My Tamron 45mm is better in this respect than the lens it replaced, a pre-ART 50mm f/1.4. But it's certainly not as good as those lenses which specifically try to correct it.
So if it's bokeh fringing which you hate, you would have to move to something like the 35 f/1.4L II. If it's fringing at the plane of focus, I still say something is off with your copy of the lens and it may be worth contacting Tamron to see if it can be corrected.
Investigating further: The Digital Picture came to a similar conclusion with the 45mm and 35mm (though the 35mm was a bit worse). I bring up the 35mm only because it's close in design and OpticalLimits.com found horrible purple fringing in their copy, at the plane of focus, much worse than TDP found in theirs. The samples at the two sites look like they came from different lenses. (OpticalLimits didn't test a 45mm.) So there could be a manufacturing variation in these lenses which leads to this. I have no idea if such a variation could be fixed after the fact.
(I don't mean to write so much in response to the comment you made. It just surprised me because I'm not seeing the same with my copy, and I was curious as to what might be going on.)