Single point. Tried groupings, but it would tend to focus on extended hands / arms vs faces.
What AF point selection mode?
Center, but the 70D, they all work great.
What lens were you using?
see below
Looking at your gear list I don't see any lens that I would pick. The 24-70 f/2.8L maybe, but, f/2.8 is a stretch for an APS-C camera indoors.
The 24-70L works great inside. We have big rooms in our house, etc., but also the Karate Studio is big too. It's a bright lens and focuses fast as well.
The 50mm f/1.8 no way, its slow old focus motor is not suited to action photography. The 35mm f/2 too wide angle for sports in my opinion.
I don't use either for anything moving.
Tamron 70-200 f/2.8 again f/2.8 is a stretch for APS-C indoors, I know Tamron's USD drive motor is supposed to be better, but, my experience with older Tamrons in the past is that their focus was awful in low light. The 100-400 L I wouldn't try indoors even on my 6D.
The new Tamron is every bit as fast as my old Canon 70-200. Excellent lens overall. Turned VC off as it doesn't have a panning mode and movements are erratic anyway. It's good for indoors at Karate as it allows for full body shots isolating my kids and at 200mm I can zoom in on their torso. Sadly, both were experiencing the same issues, thus I know it's the body. Especially since the Tamron is a tack-sharp lens on my 70D elsewhere.
Before I purchased my 6D I used the EF 85mm f/1.8 exclusively for indoors sports. Having the 6D opened me up to using my Sigma 70-200 f/2.8.
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"If you're not having fun at whatever it is you're doing, you're doing it wrong"