Invisibility makes you invisible on the physical plane only. It doesn't effect your visibility in the two other worlds: astral and Matrix. (In fact, an active spell will make you more visible in astral.) To be invisible in the Matrix, you indeed need to run silent.
On the other hand, if you're not running silent, it doesn't make you visible, it makes your icons visible. Your icons are not you. It means people can hack your devices, but they can't target you. You can't aim at someone's physical body through the matrix.
Also, to be invisible to devices (cameras, drones), you need improved invisibility. Regular invisibility is a form of mind control that only works on people with brains. (I suppose you could argue that that could still make your icon invisible to people in the matrix, but it doesn't.)