From the sudoers man page:
If set, users must authenticate on a per-tty basis. With this flag enabled, sudo will use a separate record in the time stamp file for each tty. If disabled, a single record is used for all login sessions. This flag is on by default.
In other words, disabling
tty_tickets creates a single ticket that is shared across every tty for that user. Authenticating on any tty creates a new ticket which becomes valid on every other tty belonging to that user, voila - no redundant password prompt just because you opened a new tab.
I recommend setting defaults on a per-user basis, along the lines of:
echo Defaults:$USER '!tty_tickets' | sudo tee -a /etc/sudoers.d/mycustomconf
If you really want to, I suppose, you could make a change to the global defaults in /etc/sudoers with
visudo. Something like this placed with the other defaults near the top should do:
Since the next question is usually "how can I change the session timeout value?", I figured I'd include it here for the sake of convenience:
## disable per-tty auth, timeout after 15 minutes
echo Defaults:$USER '!tty_tickets', timestamp_timeout=15 | sudo tee -a /etc/sudoers.d/mycustomconf