Unifi is meant to be a magic piece of software that sets everything up for you, but it only works to the full extent if you have every piece of network equipment as Unifi. When trying to use non-Unifi items, the magic is lost and you have to properly understand network concepts in order to set up the network properly.
VLAN tags only work to keep traffic separate if every piece of hardware is VLAN aware, and properly configured to recognize the VLAN tags. On the Network page that you shared a screenshot of, pay close attention between the items that say “USW REQUIRED” versus “USG REQUIRED”. USW means Unifi Switch, USG means Unifi Security Gateway.
For the APs: By assigning a VLAN number to an SSID, traffic leaving the AP from that SSID will be tagged with that VLAN number. There is also an option to set the management IP of the AP into a VLAN - stay away from this until/unless you really understand what is going on.
For the switches: Any network that is created as “Corporate”, “Guest”, or “VLAN Only” will be created on Unifi switches. By default all ports on a Unifi switch are set to the “All” Profile, which means it will accept traffic tagged for any of the VLANs that you set up. This is appropriate for connections to APs, Firewall, and other switches. For other ports, you should change the profile to the appropriate VLAN. For non-Unifi switches, you have to do this set up manually. Unmanaged switches come in two varieties: Some will keep and pass-through the VLAN tags, which means that when the traffic from the APs gets to the Firewall it will still be in the VLAN, but also the traffic will be sent to every port which is a security risk. Other unmanaged switches will strip away the VLAN tags, or drop packets with VLAN tags, either of which will mean that when the traffic reaches the firewall, it won’t be in a VLAN anymore.
For your firewall: If using a USG, “Corporate” and “Guest” networks will be created on the USG’s LAN port. The other types of networks are not related to VLANs. For a non-USG firewall, you have to do this manually.