I've also observed similar "jumpy cursor" behavior on Mac desktop Evernote version 7.14 (458244 Direct), OSX version 10.15.6, but in a different context. For me, it occurs when typing somewhere within a note, usually in a large note and within or near a bulleted list, which I use liberally. I haven't seen an association with single quote characters or line breaks as noted by the OP. It is an unnerving behavior, since it is unpredictable when and where the cursor will jump!
Possibly related: when typing in a bulleted list and I hit return (enter) at the end of a bullet to create a new bull