I believe this page lists the compatibility for that add on card
I don’t see the z390a listed but maybe it’s there somewhere?
I think you need to ensure that the motherboard supports the bifurcation.
I don’t know if yours does or not.
But keep in mind this only matters if you’re using bifurcation e.g. multiple m.2 drives in a single PCIe slot.
If you only need a single m.2 drive in the slot you can use simple adapters like these
Pcie to M.2 adapter
If you do need multiple m.2 and you don’t mind possibly less performance you can also use a PCIe HBA adapter that does the PCIe lane multiplexing on board and does not require CPU bifurcation, I’m using this one
High Point Rocket 1204 PCIe 3.0 x8 4-Port M.2 NVMe Switch AIC
This type of card can go in any of your PCIe slots because it does not require the CPU to split between multiple PCIe devices, it includes the PEX 8747 chip onboard to do it instead
The choice depends on how many drives you want in how many slots and what kind of performance you need between them. If you’re ok with losing your top PCIe slot and you need the performance then the Asus card you listed sounds the best. But if you only need to solve the problem of “not enough m.2 slots” these latter solutions might be easier and won’t occupy your boards best PCIe slot