Having a position “tested” or “stressed” is trader jargon for “an assumption I made when entering the position is turning out wrong and I am losing money” or “the trade is going the wrong way at the moment”.
For example: you sell an OTM option with strike K, as the underlying S approaches (and goes beyond) K that option position is “tested” or stressed. You are fearful and might consider getting out of the position (“taking max loss”), or you might stand pat hoping for a reversal by time T (“hopefully the test is temporary and I will still make money in the end”). Thirdly you might make an adjustment to your position that involves buying back the short option at K and selling another (cheaper) one at K’ farther away; this is called “adjusting the strike” or “rolling the strike”. It involves accepting that you have lost your original bet on K but taking another bet on K’ further away (“at least I get a second chance to be right”).
It is not exactly clear to me what option position is being discussed here (did you grasp that?). It may be a call spread or strangle, where one leg or side has been losing money but the other one has not (hence the use “tested side” and “untested side” to refer to the two options that make up this trade).
This kind of directional option trading has little to do with traditional quant finance. It requires accurate prediction of how S will move.