So, I decided to try charging my new cells in the TM15W, I then took a voltage reading after a few hours. To my surprise, three were at 4.15V and one was 3.63V.
The problem was, I believe, due to the leaf spring on my sample - not pushing hard enough to make contact with the head. The strange thing was, I did not hear any rattling when I shook the torch.
My first attempt was to bend them slightly upwards by lifting them with a piece of string but that failed as well - even if that worked, I would still worry that they would sag again.
Next, I took a piece of glo-ring that was lying around (which probably had cross section of 2mm and inner diameter of 19mm originally) along with a pair of tweezers, I gingerly stretch and tuck it under the springs to boost and hopefully prevent them sagging over time. Turns out, that worked brilliantly! All cells were discharged and charged evenly.
The ring tension is not enough to peel the springs up when cells are out but sufficient enough to keep itself firmly in place as shown below.
Now, I do not know how common this is or whether it should be a major concern but this solved my problem and if you guys have alternative solution, I am eager to know too.
In case you were wondering, the built-in charger terminates at 4.17V on mine.