Try cleaning the belt or remove the Japan-only seatbelt relaxer fuse.
Pull out the belt, lock it off with clothes pegs and work in a good foaming carpet cleaner.Non-retractng retracting belts will fail. Not sure why you would replace defective factory belts with some sort of aftermarket belt.
Aftermarket belts or harnesses are only road legal if they carry the ECE mark.
You can get MX-5 belts rewebbed for an economical cost; I had a pair of belts rewebbed in a colour of my choice after I discovered a cut in one of my unobtanium red S-Limited seatbelts. I used FDTS, but there are many others. As I recall, it was about £60 for two belts. They sent me some swatches so I could match the exact colour and webbing pattern, sent them the old belts, and after a week, they sent me back my Eunos Roadster belts looking like brand new.
Note, these early belts are a little different to the belt in your 95 car; I assume yours has VIN NA8C-4******
If your car has an airbag (some of those late Roadsters do), then be careful, as the belt fitted to that has a “tear away” of the airbag is deployed, essentially to make sure the airbag hits you in the right place, and not kill you.
Note, on the Eunos Roadster, there is a “relaxer” mechanism that is electrically operated; the belt automatically slightly loosens the belt when the ignition is applied. I disabled mine long ago by pulling the fuse. Sometime people think the belt is defective, because it feels loose. Its one of the 10A fuses in the internal fusebox under the steering wheel. There are a few different fuse layouts depending on the year, and these late Roadsters might have the most differences.
If you have this style of fusebox, its the 10A fuse highlighted in red
But otherwise use the translation tool on your phone (eg Google Lens) to find the fuse marked “belt”. Removing the fuse only affects the seatbelt relaxer. It does not affect anything else nor essential seatbelt function.
I do have a spare drivers belt for a late Roadster (marked late 1995) that likely needs just a clean. Pickup from the Brooklands MX5OC Spring Rally.