I have 2 of these power supplies from ebay. The first one I bought is a 145w meanwell, rated to put out 6A but actually puts out about 8.5A
It's 24v with a +/- 10% v adj pot that actually has a little more range than that. I was initially using it to charge 6S packs at 25v but I not have it turned down to 20.5v for charging 5S packs. I have an analog ammeter on it which I watched fairly closely for the first few charges and now just causually glance at it to see how the charge is going. I never saw any evidence of this hiccupping you describe, it's always shown max current until the charge is almost complete then it starts to taper back towards 0.
The second one I bought is the one linked above, a 24V 15A unit that as I said actually puts out about 18A. It's not a meanwell and I can't remember the brand off the top of my head, its more a generic name, something like JAE I think ? It also has a v adj pot but it didnt go as low as the meanwell, minimum voltage was about 22v up to around 30 max. I was a bit peeved when I first found this as I specifically bought it to charge 5S lipo at <21v but replacing the 1k pot with a 1300ohm one gave me a new range of ~ 18-30v. Nice
This one has a small fan in it that kicks in when it starts to heat up. I have an analog ammeter built into this one too (just enough depth and empty space inside the case to neatly flush mount one, or a 6S version of your balancer

) and again no evidence of the hiccupping - it goes straight to max current then tapers off at the end.
One funny thing I've noticed this one does do is that when it goes into CV mode and the current starts to fall it has spikes in current for say 10 seconds at a time. When the current falls below around 10A the fan turns off, but then randomly it kicks back in (presumably as its starting to heat up) but as it does the current goes back. So for example in CV mode if the current is around 10a the fan will kick in and as it does the current jumps up to about 13a, then the fan stops and it goes back to 10a. As the current keeps falling it does the same - current is say 5A, fan kicks in and it spikes up to say 8A, fan runs for 15 secs, then turns off and current goes back to 5A.
At first I thought the spike in current might be what the fan was using, but there's no was such a tiny little fan would draw a few amps, nor should it show up on the ammeter connected to the charges output.
So yeah theres that little irregularity, but completely different by the sounds of it to the sort of hiccupping you were describing.