'A geomagnetic storm (commonly referred to as a solar storm) is a
temporary disturbance of the Earth's magnetosphere caused by a solar
wind shock wave and/or cloud of magnetic field that interacts with the
Earth's magnetic field. The increase in the solar wind pressure
initially compresses the magnetosphere. The solar wind's magnetic
field interacts with the Earth’s magnetic field and transfers an
increased energy into the magnetosphere. Both interactions cause an
increase in plasma movement through the magnetosphere (driven by
increased electric fields inside the magnetosphere) and an increase in
electric current in the magnetosphere and ionosphere.
During the main phase of a geomagnetic storm, electric current in the
magnetosphere creates a magnetic force that pushes out the boundary
between the magnetosphere and the solar wind. The disturbance in the
interplanetary medium that drives the storm may be due to a solar
coronal mass ejection (CME) or a high speed stream (co-rotating
interaction region or CIR)[1] of the solar wind originating from a
region of weak magnetic field on the Sun's surface. The frequency of
geomagnetic storms increases and decreases with the sunspot cycle. CME
driven storms are more common during the maximum of the solar cycle,
while CIR driven storms are more common during the minimum of the
solar cycle.
Several space weather phenomena tend to be associated with or are
caused by a geomagnetic storm. These include solar energetic particle
(SEP) events, geomagnetically induced currents (GIC), ionospheric
disturbances that cause radio and radar scintillation, disruption of
navigation by magnetic compass and auroral displays at much lower
latitudes than normal. In 1989, a geomagnetic storm energized ground
induced currents that disrupted electric power distribution throughout
most of the province of Quebec[2] and caused aurorae as far south as
Texas.[3]
From https://en.wikipedia.org/wiki/Geomagnetic_storm
If this is what you have in mind, then I can see how an artificially created geomagnetic storm could be a good defense strategy, as long as everything on your island was very well shielded against its effects. Throw up great quantities of chaff continuously into the air, disguised as dust particles, and high resolution optical detection would also all but be impossible, given the disturbances of the air currents and the lightning.
And the drones themselves would have to be very well shielded. I suspect the 'other guys' are flying the drones at night, so optics is not reliable.
I am not going to comment about the feasibility of such an event, as it is not within the scope of your question. I do not know the degree of hand waving you use to dismiss inconvenient details. I will assume that you have worked it out and it can be done.
I would suspect that the drones could be detected the same way people can be detected through solid walls, by monitoring the emissions from home routers and such - not by what is detected, but by what is NOT detected. That is, a disturbance in the force. When a person walks through their house, full of wi-fi and smart phone signals, Bluetooth connectivity, and the such, the person interacts with the background field, distorting it in ways that can be picked up and monitored. That is, the field is not what is expected, but is measurably altered. The observer knows SOMETHING is disturbing the field, but not necessarily what shape. However, the sensitivity of such devices is getting more and more refined all the time, as more experience is gained from monitoring the effects of various objects. They can now pinpoint the location of a person in a room with solid bock walls, no windows or openings, by monitoring outside with a hand-held unit. This, incidentally, is a Canadian invention.
Note that it is not any emission from the person or object they are picking up, it is the background field they are measuring. They do not see what they expect to see.
It is posited that even stealth fighters can be detected in similar fashion, because no matter how well shielded, they do influence the background radiation. They would stick out like a sore thumb, not by active detection, but by passive monitors. Turns out, the billions spent on developing their stealthiness is already wasted money.
Whatever you are using to generate the storm would have to have very sensitive adjustments. It would produce known events with known effects. The field would be precisely generated to known parameters. Sensors placed around the island backed up by computers could map out the background natural field, and then would detect variations in this field, and thus would trigger that SOMETHING was where it should not be. Perhaps they could not identify exactly what, but they would pick up a disturbance.
Recall that Magnetic Resonance Imaging can map out a body by detecting the very fine changes in magnetism from blood cells rotating in different directions, in different tissues, by the disturbance in the machine induced background magnetic field.
Also think of the cloaking devices from Star Trek - the Federation could not see the enemy ship, but they could see the disturbance in the space around it. Sensor readings just weren't the way they should be.