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 bullet, sometimes the cursor jumps BELOW the newly created bullet and hitting the delete (backspace) key moves the cursor back to the end of the previous bullet where the cursor was before I hit return. It's as if the new bullet is not accessible, non-functional. I have to delete the new bullet and the line it was on and try again to create a new one, which then usually works.