Clarification on Global Modifiers

I did some forum searches and looked up the Gamepedia Wiki for Modifiers and am still a bit foggy on the particulars.

In reference to the Staff I have posted above, I am trying to figure out if all of the Modifiers(minus the obvious +2 to fire gems) will affect my character globally. An example being if I place my Firestorm and Chance to Ignite Gems in my armour, will the 40% burning damage affect it even though the Firestorm and Chance to Ignite Gems are not placed in the Staff? My question also applies to the other Modifiers listed on the staff like "Increased Fire Damage" and "Increased Casting Speed".

Thanks in advance.

Yes, all of the Searing Touch modifiers are global.

I believe the logic behind it is that none of the modifiers modify any of the on-weapon properties (physical damage, critical strike chance, or attack speed), which imply that they HAVE to be global.

So, like this weapon for example, I now understand that the modifiers should affect all attacks I make and not just the ones placed in it? Specifically the modifier that states "10% Chance to Blind Enemies on Hit"

Would a good rule of thumb be: unless stated to be specific to the item of which it is attached to, all modifiers are global? A good example of specifics towards the item would be the wand in my post here that states "Gems in this Item are supported by level 5 Blind"? I know this modifier is exclusive to the item, as it says "in this Item".

Thanks again.