Do we have different editions of the Street Grimoire?
Mine's the Second Printing and reads on Fooling Wards p.135
"It is possible to attack a mana barrier (p. 315, SR5), but doing so alerts the ward’s creator to the action, which is something the magician may want to avoid. A magician may use Flux if they have learned it, or become the astral doppelganger of a person approved to pass through the ward. Crossing the ward using either option requires an Opposed Test of the character’s Intuition + Magic + initiate grade vs. Force of the ward x 2. If the individual succeeds in this test, they are able to cross the ward without alerting the ward’s creator. If they failed, they cannot cross, but they have not yet alerted the ward’s creator. If a material link or spotter was used to generate an astral
doppelganger, reduce the ward’s dice pool by 4; if a sympathetic link was used, reduce the ward’s dice pool by 2."
So attacking is clearly alerting the mage, but pressing through isn't mentioned in mine.
The main benefit of Flux seems to be that you get your initiate grade and your Intuition compared to your Cha+Mag with the more traditional Press Through.