To activate multiple logon check when logging on using HTTP/HTTPS into an ABAP system, follow the attached SAP Note 2105302.
"Multiple logon check" in this scenario means that the system will issue a warning message about existing logons, and the user will have the possibility to cancel existing logon sessions.
There is no way to completely prevent multiple logons when logging on from a browser to an ABAP backend. This functionality is only available when logging on from SAPGUI. The explanation is that the session management for HTTP/HTTPS and SAPGUI are very different. Even when logging on from a browser only once (no multiple logon), it may result in several HTTP/HTTPS sessions in the R/3 backend, depending on the scenario. This is expected and necessary, so it is not possible to change this behavior.
The check is implemented in the standard logon classes of the ICF System Logon (Radiobutton "SAP Implementation" in the SICF System Logon settings). It is not necessarily implemented in custom logon classes (Radiobutton "Custom Implementation" in the SICF System Logon settings). For example, multiple logon check is not implemented in the logon class /UI2/CL_SRA_LOGIN used by Fiori.
Note that opening new tabs in a browser does not count as a separate logon. Browser tabs are sharing logon data amongst themselves, so the ABAP backend has no means to differentiate which tab the request is coming from. This is not an SAP specific behavior - it is the way browsers handle logon sessions.
SAP Note 2105302: Multiple logon check based on security sessions for HTTP/HTTPS login into an ABAP system
SAP KBA 1841303: Multiple Logon Restriction in case of webgui / ITS with parameter login/disable_multi_gui_login