I guess different HA’s might work differently in detecting a magnet but with my ReSound Quattro’s, putting on my Surface Headphones would cause the Quattro’s to think that I was putting a landline receiver to my ear and the HA’s would switch to the Acoustic Phone (old-fashioned landline) program. Since I didn’t need the old-fashioned landline program, I removed it from my HA settings (DIY) and then I no longer had any problem - nothing funny happens - when putting on my over-the-ear headphones. Perhaps something similar happens with your HA’s and if a landline, magnetic phone program is active and you don’t need it, you might want to consider turning it off (or have a provider turn it off) and see if that cures your problem.
In the post referenced below, I mention that there are lots of other posts on the forum going back at least to 2011 about headphone/HA problems so there might be some very useful info in some previous forum posts: