A trigger placed in the editor will always run on all machines, so there shouldn't be any need to use publicVariable to make them MP-compatible. A simple vel = 12
in the activation will record the value on every machine.
The only time you need to use publicVariable with a trigger activation is if the activation calls a script that is only to be run on the server (e.g. has if (!isServer) exitWith {};
or ? !isServer : exit
at the top of it), which then publicVariables a value so that all machines can see it.
There are reasons for dealing with triggers in either way in MP. It really depends on the situation (but you might as well try the simpler method first and if it doesn't work as you'd like to, consider the latter one).