The core book says that astral perception is done by assensing, which is a sort of psychic sense. Tradtitionally in Shadowrun, this has meant that illusion spells like invisibility did not affect astral perception. They might decieve your vision, but since you don't use your vision on the astral, it doesn't matter.
But all the book says about spells on the astral plane is that only mana spells work on the astral. What does this mean for mana based illusion spells? Do they still work? Sure, invisibility affects your vision, but it's not like it targets your eyes, or even the vision center of your brain. It targets your "mind," erasing the mage's visual presence from it. Or does it? If it did, then you wouldn't be able to "see" the mage with ultrasound... right?
I would say "I sure hope the magic rulebook clears this up," but it's already been published and it's no help