This problem happens on MacOS using version 5.1.7.80 of the Cisco Secure Client – not sure how it behaves on Windows or Linux.
If one stops sharing the internet connection from the phone to the computer which is connected to VPN using Cisco Secure Client before disconnecting the VPN connection on the computer first there will be some annoying behavior.
Cisco Secure Client tries to reconnect, but of course it can't since there is no connection to the internet.
At this stage eventually the ”Cisco Secure Client - Web Browser” brings up a window showing info about the Meraki security appliance:

Now, if one tries to close that window it will come up again.
If once tries to disconnect the connection to the VPN in Cisco Secure Client via the app or the icon in the menu bar it disconnects, but after one gets connected back to the Wi-Fi network no sites can be browsed – in Chrome a ”ERR_INVALID_HANDLE” message comes up. One way to resolve it is to go to the System Settings and the network preferences for the network interface in use and ”Renew DHCP Lease” in the TCP/IP section.
I think the internet connection being cut off while being connected to the VPN should be handled better by the Cisco Secure Client. While people mostly disconnect the VPN connection before stopping the shared connection from the mobile phone it can happen that the connection gets cut off and then there is too much hassle to get back to being connected to the Internet via Wi-Fi.