The rule I was taught at school was that either is correct but you must use whichever you pick consistently. NB it has nothing to do with the double s at the end, the same rule applies to James or Thomas.
The rule I use at work (editor ) is dependent on whether the 's' in the word when spoken has an 's' or a 'z' sound. So it would be Jess's cat but Jess Jones' cat. Because 'Jessiz' sounds fine but if you added apostrophe s to Jones it would read 'Joneziz' ie the two 'z' sounds are a bit much together. I don't think the double s matters here.
I've no idea if that is standard use or not though and my copy of Fowler's is downstairs.