No, not correct. FiOS DOES NOT USE MODEMS. FiOS uses routers.
Verizon routers plug into coax to create a MoCA LAN, which is quite different than the DOCSIS WAN that Cable modems use to communicate with the headend. Verizon routers get their WAN connection using the Ethernet WAN port on the router connected to the Ethernet port on the ONT, although older/slower installs may use coax for a MoCA WAN connection instead of Ethernet. MoCA WAN is a separate network from MoCA LAN, even though it's on the same coax.
In short, do not plug a cable modem into coax on a FiOS system, it will not work.
The device you have does not appear to have anyway to separate the router function from the cable modem function. If it did, you'd be able to plug the Ethernet from the ONT into an Ethernet WAN jack on the router. But it doesn't have an Ethernet WAN jack based on the pictures I saw of it online. This means it can't be used as a gateway router for anything other than a pure cable system.
You can use a non-Verizon router. If you have older Verizon set-top-boxes you'll need to create a MoCA LAN for them using the adapter you found - plug it into a LAN port on the router and the coax network. You may need to open some ports to get guide, on-demand and other functions working - check out the FAQs at Broadband reports.
If you have the latest boxes; "FiOS ONE," my understanding is they must have a Verizon router present for activation. Keeping them running may require periodic updates to port settings. Lots of posts on this forum and the dslreports FiOS forums from people who try this.
Further, the use of a non-Verizon router is completely unsupported by Verizon. If you have issues with any equipment other than the ONT, they will not help you. This includes issues with the set-top-boxes. For internet only users, this isn't too big of an issue. Many TV subscribers who use their own router keep a Verizon router around to plug in should issues occur so they can get support.
In short, if you have Verizon set-top-boxes, it is easiest to use their router. If you don't, at least keep one around in case problems occur.
You don't have to rent the Verizon router. You can buy one from them. A new WiFi6 router just became available and sells for $299. The older Quantum router is not for sale new from Verizon anymore, however you can find lots of used ones online for under $100. Just be sure the seller has a return policy you can live with. If a Verizon router was ever connected to a Frontier network, it will have Frontier firmware in it and won't be recognized as a Verizon router by their system. The only way to confirm the firmware version is to check via the router web page.
P.S. Sorry for the all caps, bold text at the top. It's just this question comes up very often and it needs be stated loud and clear that modems have no place in FiOS.