The three most recent wars appear to have had different aims/goals/causes but it's important to realise that the Vorlons and Shadows have been at each others throats for hundreds of millennia. Pointing at any specific event as being the "cause" of an attack is to ignore the centuries of buildup.
1 (Circa 8,000BC).
In this war, the Shadows and Vorlons openly opposed each other. This war appears to have been largely triggered by the Vorlons creating an alliance with the Minbari and sharing technology but it's hard to say who struck first. There's also some chatter about the Shadows regaining their strength and the damage caused by an earlier combined attack from the Vorlons and the other Elder races.
2 (Circa 1000AD)
This war seems to have been caused by the Vorlons actively seeding planets with telepaths. The Shadows then attacked and occupied as many of those worlds as possible (including Narn) but it's notable that a state of cold war had existed for thousands of years before, with the Shadows covertly attacking/supporting the younger races in order to keep them bickering among themselves.
3 (Circa 2260AD)
This latest (and last) round of conflict was was triggered by the Icarus landing on Z'ha'dum. This action, and presumably the fact that IPX was an interplanetary organisation) seems to have convinced the Shadows that the Babylon Project; uniting the various powers in the galaxy, was a clear and present threat to their goal of evolution through conflict. Even then, it was only down to the action of Sheridan that the Shadows were brought out of hiding and exposed as the architects of the present conflict.
JMS has shared his thoughts on the Shadows and their motivation.
Q. ... why are they [the Shadows] attacking the younger races directly?
JMS: Well, look what happened when the shadows came out and attacked a couple of places...first they did so without anyone knowing it was
them doing it, as we've shown. So now everyone's running around like
ants, scurrying for cover and trying to figure out what the hell's
going on, accusing one another...then the Centauri got the
credit/blame for it, causing further conflict...then they came out and
sent everyone scurrying again, some to make alliances they thought
would protect themselves (and thus enable them to make war on their
neighbors, as shown), only to have that fall apart and they turn on
Q. Aren't the Shadows defeating themselves by giving everyone a common enemy?
JMS: Nope. First they attacked careful to not let anyone know who was doing it, so they'd accuse each other. Then they'd let another take
the credit/blame for it, the Centauri in this case. That'd spin off
new alliances and new...wars, and everyone's scurrying for cover. THEN
they reveal themselves, and now you've got re-scurrying, some who try
to make deals, and then attack others (as stated) thinking they have
an unbeatable ally....most of the killing up until this point was done
by the others, not the shadows. This current campaign would also lead
to scattering the pins, and watching as they restructure, and they'd
pull out again to let them scurry...and keep chewing at each other,
only coming out when necessary to tip things over, then recede again