Some correction is in order here.
USB power supplies actually don’t controll the charging of the battery at all.
All they do, is provide a negotiated voltage up to a given current. By default, that’s 5V at 900mA (=0.9A) for USB 3, or 5V at 500mA for USB 2.
USB PD (which stands for Power Delivery, not Power Direct) can be used to negotiate up to 20V at 5A. This only happens, when a USB PD negotiation is successful, so this cannot harm devices that don’t support USB PD. In that case, it falls back to 5V.
The voltage is supplied by the power supply, but how much current (ampere) is actually used is determined by the device. The ampere ratings of the power supply don’t determine how much current flows, but what’s the maximum amount of current, that can be drawn safely.
Overcharge protection, same as the charge process in general is completely managed by the phone and has nothing at all to do with the charger.
Otherwise, phones would blow up each time you connect them on a dumb charcher which just supplies 5V and leave them there over night.
To prove the point, I’ve got a non-USB power supply here, that supplys 5V with 11A at maximum. That’s about 12 times as much maximum current as USB 3 normally supplys. I cut up a USB cable and connected it only to the 5V output. So here we got a supply, that can supply crazy amounts of current at regular USB voltage, but with no USB PD negotiation.
When I connected it to my phone, it totally worked, and charged my phone. At 0.9A. The reason is, that, since there was no USB PD negotiation, the phone didn’t know the capabilities of the power supply and thus fell back to only using as much current as it knew would be safe: USB 3 standard 5V@0.9A.
TLDR:
- A power supply cannot overcharge a phone battery
- A higher power USB certified power supply is always safe, even when plugged into devices that don’t support USB PD (except if the power supply is defective or something)
- A power supply supplys power. It does not even know that there is a battery charged by it, and it certainly has nothing to do with the charging process.