You might also read thru the main 'top balance' thread here as well:
For current best practices on top balancing cells, please watch the video and download the PDF at the following page: Top Balancing Cells Using a Low Cost Benchtop Power Supply If you are interested in a more general tutorial of what balancing is about and *Why* to balance, check this out...
diysolarforum.com
Not sure why your amperage output would 'jump around'. Current should taper off as the cells reach full charge.
I got the same brand power supply, next model down with 2 display lines and no usb port. 10A - 30V adjustable. Worked just fine. $59
But parallel charging can take a LONG time depending on charge state - whatever your cell capacity is you multiply that by the number of cells in parallel. My four took 4-5 days. Mine sat at that 5A current level for several days - notice I have volts set to 3.4V. I thought I would do this in steps, or stages - takes way too long. I finally reset the voltage to the full 3.65V, with a DMM, not the unit, and let the cells fully charge to zero amps. Set power supply voltage THEN connect and turn on - don't adjust voltage while it's charging.
To speed up the process you can connect them in series to 12V for regular charging, to get them closer to full charge. A BMS is required to make sure you don't over charge any cells. If you can find the specs on the Battery Tender charger then you'll know if it will work - usually those are a fixed 14.4V or so on the absorption charging stage. But I would be surprised if it is more than 10A as well. So yeah, charge them up to 3.5-3.6V per cell, then rewire in series and do your top balance at 3.65V per cell.
Your power supply will also charge them at 12V nominal, so that's another option. You just need to watch them and stop charging when they reach full charge - if any cells reach over-volt your bms will shut down charging. You might shoot for 3.4 or 3.5 with series charging, then re-wire to parallel to top-balance.
It is recommended to make up new charge leads with 10G wire and ring terminals for your power supply and to the battery. The supplied wire with banana plugs and tiny alligator clips creates a lot of resistance at 10A.
Mine sat like this for 3 days and I thought something was wrong. LOL 230A @30% SOC X 4 = 644Ah. At 8A average that's 80 hours, three and a half days.