Yes, there is now an (un)official statement
Jeremy Crawford has clarified in a Tweet:
Q: A firbolg PC casts booming blade then uses hidden step to go invisible. The creature that is hit with booming blade moves away and
thus takes damage. Does hidden step deactivate?
A: Hidden Step ends if you make a damage roll, no matter when you make
Q: So it doesn't matter if a spell/effect is initiated by you before
hidden step was activated? As long as you make a creature do a saving
throw or attack or roll damage for any reason then hidden step ends?
A: That's correct.
So, passive or not, as long as a creature is making a saving throw or taking damage from an effect you initiated (no matter when you initiated it) for any reason, hidden step will end.
This matches the intent we can understand when reading the ability itself.
Intent is clear from reading as well: if the user causes a harmful effect, hidden step deactivates.
The ability is explicitly written to restrict just about every way you can damage or harm an opponent (regardless of when said effect was initiated), so it seems clear that the intent was to prevent the user from doing harmful things. As such, allowing a loophole for spells and effects cast/initiated before the user used hidden step runs counter to that intent.
It may also be helpful to note that the designers also intentionally wrote this ability so as not to restrict beneficial spells and abilities being used.
The ability is already quite powerful and from a DM standpoint this argument would seem like an attempt to cheese additional power out of the ability by circumventing its primary restrictions.
This also seems wholly fair. In the example of booming blade, the only reason to cast such a spell is to try to cause damage. If you also choose to use hidden step you are taking the risk that the opponent triggers that damage and thus cancels your ability. It was player choice to cast the spell and to use the ability.
Allowing this opens the door for plenty of bad things/cheese
Our heroic firbolgs casts delayed blast fireball at a group of 4 enemies, uses hidden step, then immediately stops concentrating on the spell. It takes no action to stop concentrating on a spell so this is the exact same scenario as with booming blade. This causes 4 saving throws and 4 creatures to take up to 12d6 damage.
Does it seem to be intended to allow such an effect to not break hidden step? This seems like an overtly harmful action and I really do not think for one second that the designers intended this to be the case.
And this is only a cursory look at one spell. I'm sure that there are many more and possibly even worse spells/effects one could get away with through this loophole.
Neither RAW nor RAI support allowing a loophole for effects initiated before hidden step is activated.
As always, a DM may, of course, allow this if they want to for any reason.