To everyone who's Smarter than a 5th Grader?

I watched the game show 'Who's Smarter than a 5th Grader' recently and came across this 4th grade grammar question:
"What part of the sentence is the last word of the following sentence,'The paint spilled everywhere.'"
Guess! What is the word class of 'everywhere'?

It's......ADVERB! Applause to everyone who got it correct!
(FYI, the contestant thought it was a noun. Thankfully she was saved by the 5th grader)

In this case, 'everywhere' is an adverb because it modifies the verb 'spilled', describing where the paint spilled (tells us the place where the action is inflicted upon).

This set me thinking, what if the word 'everywhere' is placed in another part of a sentence. For example, in the following sentence, "Everywhere we went, the dog followed us," is 'everywhere' still an adverb, probably describing the verb 'went'.
So I checked the Macmillan English Dictionary for Advanced Learners, it states 3 different ways the word can be used, as an adverb, a pronoun or a conjunction.

In the example above, 'everywhere' is a conjunction because it joins two clauses together, 'the dog followed us' and 'we went'. I can reorder the two clauses to make the conjunction in the centre like this, 'The dog followed us everywhere we went.'

As a pronoun, 'everywhere' would be used like this: 'Everywhere is very quiet.' This is because 'everywhere' here replaces a noun or noun phrase of a place.

Hmm since, 'everywhere' can have 3 different word classes, what about the word 'everyone' like how it is used in the title of this post?