My story progression is currently off. However, when I look at the household funds of inactive families, they get bigger and bigger the more I play with my active family. I really don't like that - when I switch back to them they have so much money, which takes away all the fun of playing them until they're rich.
Is this normal for the game or is my story progression somehow not really turned off? And if it's normal, is there a mod to turn it off? So far I haven't found one.

.... i don't think story progression being off is supposed to stop them from earning money at their jobs, It just stops them from getting raises and promotions. To mess with money try Nraas mods (taliwans mods) between Master controller, overwatch, story progression and register you have 100% control over every aspect of your town and its inhabited, There is a lot of options and Tali used a lot of weird terms for things so it takes some getting used to. There can be 4 different options that control the same aspect in a different way. He has retired but there is a great team over at the Nraas industries discussion page who answer all the questions. I don't work there but i do frequent the help section there too. Hopefully the new team makes it a little more ui based and less of a 200 levels of lists lol. Love the mods tho, Im kind of a sims town control freak, wouldn't play sims 3 without those 4 key mods.