Having installed hundreds of cold weather kits, I can say I've had to strip some of the heat shrink off the tip of the wire harness on at least 50% of them, or they do as you said, pop out!
My harness had about 1/2" of tinned wire sticking out past the heat shrink---Just enough to engage and stay retained. I was worried that when I pressed on the retainer to insert the harness, that the N1 or N2 wire would pop out and short against the compartment wall, but those 2 wires did not move at all. I did not want to turn off the main breaker in the transfer switch and kill the house---too many things to reset, and I was afraid to use the fuse puller that comes with the transfer switch for fear of breaking the glass tubular fuses. I owned 3 service stations for 45 years and I remember trying to pull tubular glass car fuses with a puller that grabs the glass---It did not pull the fuse---It broke the glass and then you had to pry the caps out with a small screwdriver !!! It was easier to pry a cap out of the fuse holder prongs and then just grab the fuse with your fingers---But that was 12 volts, not 120 or 240 !!!