You are learning a lesson that many people have learned:
1. unbalanced cells
2. charged in series
3. without automated protection
4. may look fine at mid SOC
5. but can go screwy rapidly towards the top or bottom
Some notes for the future.
Your charger didn't react because it probably did not know it needed to. A BMS handles cell level safety, a charger is only aware of pack level voltage, and because your pack has not been balanced pack level voltage will not necessarily reflect cell level voltage (as you experienced). Even with a balanced pack, pack level voltage should not be assumed to be an accurate proxy for cell level voltage. As an example cell voltages of [4V + 3.5V + 3.5V + 3.5V] /4 = 3.625V avg, which is a safe voltage as far as the charger is concerned, since it can only see the total pack level, not individual cell voltages.
As a general pointer, patience and/or extreme attentiveness are the best approach to top balancing. Most of the issues we see here, come from people trying to speed the process up (either by an unprotected series charge or setting the voltage too high and not actively monitoring with a parallel charge).
The good news is, you caught it at 3.9, and a single cell exceeding 3.9 for a few minutes is probably not a huge deal in the realm of things.
From what I have observed, people that follow these three guidelines (and one honorable mention) have to work a lot harder to damage a cell:
- Never charge in series without a working BMS
- Never set your power supply above ~3.65 or 3.70 when charging in parallel
- Know how your power supply works, and set the voltage before connecting the cells
- Honorable mention: Be present and attentive when charging in parallel above ~3.45 or 3.5 or so
Follow these 3 (well 4) guidelines and chances of damage are very small. More experienced or less cautious folks will sometimes not follow #2, I'm not saying its wrong to do so, just that it increases risk that could be easily avoided. What I am saying is for everyone, but especially beginners, following these guidelines significantly reduces the chances of error or damage (at the expense of a little extra time and effort). My anecdotal observation is that almost every problem with top balancing I have seen on the forum has been partially or fully explained by one of these 4 factors.