I'll disagree with Camilo Rada's answer, and show that there is definitely a magnetic anomaly.
We start with the interactive geophysics map of Geoscience Australia, Australia's federal geoscience agency. Our region is this:
Here's the same area with magnetic intensity layer turned on:
You can see a clear magnetic anomaly in this area, and it's actually much more widespread than noted on your map.
If so, is there a naturally occurring phenomenon…that causes it?
In general, answers to questions like these are yes. But let's explore it further with the geological map of the area:
Overall, the rock type around is "OSn" and "Os". According to the legend, these are high grade metamorphic Ordovician and Silurian rocks, and neighbouring rocks are siliclastic which tells me they shouldn't be too magnetic (confirmed by the magnetic map). The area of Mt Jim has "Dg" (= Devonian granites) which might be slightly magnetic. But here's the thing you were looking for: "Czb", which is short for Cenozoic basalt. And basalts are magnetic.
So to answer your question, the source for the magnetic anomaly isn't a "submerged" (buried would more appropriate here btw), but a basalt fully exposed on the surface.
Interestingly, the blog post mentions the presence of basalt, so it's not entirely clear why they claim that there's a "massive, yet unknown, submerged object". Most probably there's simply more basalt, or its intrusive analogue: dolerite or gabbro. These targets are attractive for the mining industries. I would be surprised if it hasn't been drilled at some point by an exploration company, and then the underground cause of the anomaly would be very well known (but probably not publicly).