Yeah there are two things there.
If Jo not there...then yes she will, but she will give you the money anyway if forgive her. However, even if Jo not there, IIRC, you can not call the security office, been a while since last played that section, can't recall if that's forced or not off-hand.
If Jo there though, she will not be added (even if dating Bella IIRC) as you ask Jo to do it for you if memory serves me correct. I could be getting mixed up there though with the chain of events. Key aspects though are, always let Jo stay at the beach house and always give Elaine the house.
Ofc, that's all providing Cheeky doesn't change that little
loophole with his little rewrites, I hope he doesn't though, pretty sure being able to do that was written intentionally (cos...screw you Don hahaha).