Verrencia Shield linkers share shield HP with phase shields and other shield linkers within range. They also prevent the shields from dropping entirely while the linker has shield HP. Shots that exceed the shield's HP can penetrate, but not if they explode on contact like missiles. Large twin cannons and nukes have enough AoE to deal serious damage from the shield's edge. Sufficiently large mass drivers and railguns can penetrate. Anything else has to wear through the whole HP pool or deal damage in one linker's domain faster than other linkers can share HP with it.
There are two probable reasons your testing misleads you.
Under AI control your ship will pick a single part to target and hit one or two shields, which can't go into negative HP. Before they can be checked for going down they get the linker's HP shared with them. The missiles explode instead of penetrating because when the shield HP are too low because they're AoE weapons and that's how AoE weapons interact with shields. Tested without the AI, your missiles will go everywhere and do closer to their rated damage, but as a BH NPC they will always be under AI control and target a single part. There is a comment in the code that Kroom thought this overflow would be taken from elsewhere but was not certain. I think your ship empirically answers that in the negative.
In a realistic scenario, ships start more than 270 meters apart. Your missiles will not fire all at once, but spread over the time it takes your ship to move its own length, which since the AI is braking as hard as it can to avoid overshooting its desired target distance is considerable. The stream appears continuous so it must take at least 2 seconds for all the launchers to pass the 270 meter mark. This is long enough for every shield linker or three shields to regenerate the rated damage of one missile, of which most is lost to overflow.
More powerful shields from other mods don't have these interactions unless they are also using multiammostorage.