The power bank consists of battery cells and built in charging circuitry that monitors the cells and controls the charge and discharge. That built-in circuitry will terminate the charge when it is full (or shut down the power bank when the cell voltage drops too low) regardless of whether it is still receiving voltage from an external source.
The Aukey or Apple charger is merely providing voltage and current to the power bank, it is not controlling the power bank. Some USB chargers do have some "smart functions" and the Aukey in your link claims to prevent overcharging but the TQKA wouldn't be aware of that and is designed to make its own determination as to whether it is fully charged.
The charger is merely supplying the current and voltage it is rated to output. Just because the Apple charger is supplying 4.96 volts when connected to your TQKA doesn't mean that the power bank will charge its internal cells beyond their rated upper limit of 4.2V. The power bank's internal battery charging circuitry will manage the incoming voltage and current. This is the same thing that is happening when you charge your iPad Air with this charger. It is circuitry inside the iPad Air that is controlling the charge to its own internal battery just the same as the TQKA is controlling the charge to its internal cells.
I have some bad news to report about my TQKA power bank.
After purchasing the TQKA this winter and testing it out thoroughly I decided to put it away until the warmer weather arrived before using it in my vehicle. For the time being, my standard lithium-ion battery backs seemed just fine operating for long periods in my vehicle here in New England when the winter temperatures were still quite cold. Not that I've had a problem during hot summer months using lithium-cobalt power banks mind you, but LiFePO and lithium-polymer (as opposed to 18650 celled power banks) seem a good hot weather alternative.
The standard recommendation for long term storage of lithium batteries is to keep them at about 50% charge, so that's how I always keep power banks that are not in daily use.
So, I had two 20,000 mAh power banks that I put in storage at the same time until they were needed, both charged to 50%. One is a PowerAdd Power Pilot which is essentially a single huge lithium-polymer cell. (also safer for warmer operating conditions) The other, of course, is the TQKA LiFePO. When I recently went to check on these banks that I last used in early March, the PowerAdd was still at 50% charge and the TQKA was stone cold dead......0%!
I gave the TQKA an overnight charge and it's back to 100% and seems fine (for the time being) but the fact that it lost all of its juice is worrisome and certainly not a good sign.
I need to do a bit of research and find out more about long term storage of LiFePO batteries.
I still haven't used mine much but think I used it to charge a phone 2 weeks ago. It is currently reading 78%. But I don't think it works this out from the cell voltage. It seems to track how much power has gone out through the ports, deduct this from the theoretical capacity, and calculate what SHOULD be left.
There are two flaws with that. The cells may not have the capacity they are supposed to (especially when old.) And it doesn't take account of self discharge. So when it gets low it can jump from, say, 20% to 0% really quickly.
And trying to store it at 50% charge would be risky if the reading is inaccurate.
I'll do another discharge test without recharging first.
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Power banks have circuitry that measures SoC (state-of-charge) internally, not by how much power has "gone through the ports".
That is my point. The former is what you need and expect, but my tests do not match that.
E. G. So far today my Tqka has gone down by about 10% according to the display, and pumped out about 6.4Wh according to my USB tester. That's 10% of the claimed 64Wh capacity. Perfect! Too perfect, though. I know it only gives out about 50Wh. We'll see what happens next.
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Interesting facts, but as it only cost £20 delivered.
It is what it is.