Adverbs of quantity tell us about the degree of something. They are usually placed before the adjective, adverb, or verb that they modify. The words "too", "enough", "very", and "extremely" are examples of adverbs of quantity.
In the example you gave, demasiado is telling us the degree to which the bosses are strict.
Following what Marsha explained, you can also have the word "demasiado" as an adjective, but this is when it is modifying a "noun", in which case the adjective needs to agree with the noun in gender and number:
He comido demasiados helados.
I've eaten too many ice-creams.
Here is the Wikipedia definition: "An adverb is a word or an expression that modifies a verb, adjective, another adverb, determiner, clause, preposition, or sentence". [< That applies in the English language as well as in the Spanish one, and in many others too].
The word "adverb" does look appropriate when it is modifying a verb, but perhaps it sounds a bit odd if it is modifying an adjective. It is nevertheless the correct term to use in both cases.
So we could perhaps regard it as a name-giving 'peculiarity' - but we just have to accept it.
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