"...projects an illusion that makes you appear to be standing in a place near your actual location, causing any creature to have disadvantage on attack rolls against you..."
Your answer is implied by the the language of the description, the key point being the 'cause and effect' that it describes. The item description says that the disadvantage is CAUSED by the illusion. So, if the illusion does not work, neither does the effect caused by the illusion. If "A ==> B", and their is no A, then there need be no B.
There are numerous reasons why the illusion might not function as expected, two possible cases of which are:
A) Perhaps the process is taking place in an antimagic field that prevents illusions from bring projected - in that case, no illusion causes no effect of the illusion.
B) Perhaps an attacker has a sense (blindsight, truesight, tremorsense, etc) that allows them the effects of 'seeing' the target w/o relying on visual sight. Again, then the illusion does not function for them, and since it is the illusion that causes the disadvantage, no disadvantage.
I read in an earlier post that someone was speculating perhaps the illusion functioned by directly affecting the mind of the viewer. Were that the case here, there would be a saving throw (Wis, probably), and possibly charm immunity would foil it. Since nothing like that happens, the effect must be external to the mind of the viewer, and hence is a mere visual projection.