Your OP mixes up several terms, which lead to some replies that probably aren’t specific to your question.
A Multispectrum Shield Hardener is a resist module. It makes your shields more resistant to damage, ie., they take less damage from a hit of any type that they resist. So for a Hardener, you want it on as early as possible. Every hit that you allow in without turning it on does more damage than it otherwise might.
That’s why you get “effective” HP, not real HP: if you have 1,000 shield HP and incoming shots do 100 HP damage each, your shield can take 10 hits or 1,000 HP of damage. If your shields offer 20% resistance to the incoming damage, then each incoming 100 HP of damage only removes 80 HP from your shield. Your shield now lasts for 12.5 incoming hits or 1,250 “effective HP”, even though it still only has 1,000 shield hit points.
A shield extender actually adds base HP to your shield. So an 800 HP Medium Shield Extender would increase your shield from 1,000 to 1,800 base HP, but it would still take full damage from each incoming hit unless you add resistance modules. It is a passive module so would not be activated or on-lined in mid-battle (in general).
You can think of any “resistance increasing” module as a “Current Hitpoint Multiplier”. It increases the ‘effective’ amount of any HP you currently have by reducing the incoming damage. So it has greater effect the more HP you already have.
An Assault Damage Control gives passive resistance that’s a little lower than a regular DC. However it can be activated to give much stronger resistance for a short time, 10 seconds IIRC. So you would generally activate when you need 10 seconds of greater protection, not based on your “current” HP. Eg., when you need 10 seconds to escape, or to resist 10 seconds worth of very high incoming damage while you whittle down the opposition. Or to give your active repair 10 more seconds to build up more HP, etc.
So hitting activate on your ADC right at the start might not be wise (your active repair might be enough to negate incoming damage at that point, or the incoming damage might no be high enough to need it). But activating it at 1% armor left also won’t be wise - as you say it won’t magically add to your current HP.
It’s complicated to picture it all at once, but understanding the full interplay of your base HP (shield/armor/hull), their native resistances, active repair sources, passive regeneration (for shields), resistance modules; and balancing those against incoming damage while you work to remove the sources of incoming damage, is the end goal. It helps if you can envision 3 graphs and a threat-priority point-plotter in your head simultaneously.