Hello, I tried to change an attachment to multiply mode and export a json and atlas. It worked fine.
I will need more details on how to reproduce your problem, can you provide an example file, or gif/video showing what happens please?
You also mention PSD in the title, but talk about slots and Spine version, I tested this in Spine, does it need to be tested in Photoshop instead?
I just tested in Photoshop and the export was fine, so it's likely not the multiply mode that is causing the problem.