MoCA was specifically designed with the ugly reality of existing home CATV/TV-antenna 75Ω coax cable infrastructure in mind. So it's designed to work across multiple splitters. It absolutely does NOT require that the adapters be connected to an isolated point-to-point coax, or tapped off the same linear coax bus, or connected to two legs of the same splitter. But there must be some kind of coax path between the two devices; it's usually expected to be a small hierarchy of splitters.
The basic assumption is that you have one coax cable coming into your house (either from a cable TV provider or an aerial TV antenna on your roof/attic), and that cable feed is split, through some small hierarchy of splitters, to all the coax jacks where you might want to hook up a TV.
So in your case, regardless of whether your cable feed goes to your family room splitter first, and then a leg from that splitter goes down to feed the basement splitter, or vice-versa (cable feed comes into basement splitter first, and then a leg of that goes up to feed the family room splitter), or even if both the basement splitter and the family room splitter are fed from another splitter closer to the point-of-entry where the coax line first enters your home, MoCA will work across any of those splitter topologies.
It is worth noting one quick/cheap/simple improvement you can make to your home's TV coax cable infrastructure to help with MoCA: Install a "MoCA POE filter" right before the first splitter your coax cable hits as it enters your home. POE means "point of entry" in this context; it's designed to be installed where the coax enters your home, more or less (that is, right before the first splitter on your premises). This filter not only prevents your MoCA signals from leaking out onto your cable provider's coax network, it also reflects your MoCA signals back into your home's coax tree, helping the MoCA signals propagate across the splitters in your home.
When the people developing MoCA started testing out early MoCA designs in real world homes, they found that if two MoCA devices couldn't talk to each other very well between two arbitrary coax jacks in the home, a very high percentage of the time, adding a MoCA POE filter at the top of the coax tree was the only intervention that was needed to get things working acceptably.
If you have additional budget to spend on coax cable infrastructure improvements to make MoCA work better in your home, the next thing to do is to look at what frequency range your splitters are rated for, and for any that don't state that they are rated all the way up to the top end of MoCA's frequencies (2GHz?), replace them with ones that ARE rated for frequencies all the way up to the top end of MoCA's frequencies.
MoCa is used more frequently for DVR and other multimedia devices provided by cable companies. OPs details does not indicate they are connecting computers to this, just a home cable TV setup. Further, the question is "have I set this up correctly" and does not indicate they have tested anything, meaning the question is lacking information. – music2myear – 2018-10-24T16:09:53.563
1@music2myear MoCA is for doing home LAN networking via a home's existing CATV/TV-antenna 75Ω coax cable infrastructure. I don't need to know the nature of the other devices on his home LAN, or what he's tried, to tell him that Yes, it'll work across multiple splitters. – Spiff – 2018-10-24T17:34:42.957