Yes, removing the not will add the money to your own treasury when you're playing as the Julii.
As to making it work, the multiple seasons should pretty much always go at the bottom of your background script.
So try something like this:
Code:
script
;declare counters
suspend_during_battle on
declare_counter loop
set_counter loop 0
;money script
monitor_event FactionTurnStart Treasury < 10000
and FactionType romans_julii
and not I_LocalFaction romans_juli
console_command add_money roman_julii, 10000
end_monitor
;Multiple seasons
console_command date -272
console_command season summer
while I_TurnNumber = 0
suspend_unscripted_advice true
end_while
....
while I_CompareCounter loop = 0
end_while
end_script
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