Does a globe of invulnerability protect from wall of fire depending on where the caster is?

What happens if a caster casts Globe of Invulnerability, then a second caster casts Wall of Fire such that the first caster, still inside the globe, is inside of the wall?

Does the first caster only take damage from the Wall of Fire spell if the caster of that spell is also inside of the globe? Or does the Wall of Fire not effect the first caster at all no matter what? This sentence is the one I’m having trouble with:

Similarly, the area within the barrier is excluded from the areas affected by such Spells.

I’m not sure if that overrides the restriction of being inside of the globe or not.