It doesn't seem a software bug. When battery voltage is very low, charger control IC will not use high speed charging. A reason is that battery can be faulty. Putting maximum current through that battery would be a risk of explosion. Only when battery voltage increases to a certain level, controller switches to the full speed charging. It is where your problem is starting...Had quite a big skrik with my iPad 4 last night. The battery was quite flat think 6% and when I plugged it in to charge nothing happened. I first confirmed that the charger works by plugging in my iPhone but it was fine, then I also tried another charger with another lightning cable but still no joy. I switched off the iPad and then when I plugged in the charger the Apple came up on screen *sigh of relief*, then I switched it on and it was charging just fine.
This must be a bug in the new iOS 9.3 because just 3 or so weeks ago when I also ran down my iPad battery very low like 3%, it charged just fine.
I think your chargers are not able to give sufficient current (rated for this charger type) and voltage drops below limits. The worst case scenario is when battery is low but not completely flat so battery can be charged with a maximum current for this particular charger. When you switched phone off, requirements for power was reduced, increasing voltage on the battery.
I suggest to test your chargers under full load and meassure output voltage. Typical fault in MOSFETs is an increased resistance. Apple might tweak trigger values with software updates, so hurry up and replace substandard charger before it happen.