First, let me say that, while punctuation and grammar are related, details like commas don't generally make something ungrammatical.
You can find lots of guidelines online that explain how to use punctuation, but you need to understand the terminology that the guidelines use in order to apply the guidelines correctly. I am guessing that you are referring to something like this:
Do not use commas to set off essential elements of the sentence, such as clauses beginning with that (relative clauses). That clauses after nouns are always essential. That clauses following a verb expressing mental action are always essential. Purdue
In this case, essential is not a standard grammatical term: I suggest that it means that the sentence wouldn't really make sense without the clause. Imagine removing the bracketed clauses from these sentences.
I know a man [who can help you].
I told him [that I wasn't free tomorrow]
I think [that it's time for lunch]
Looking at your sentence,
Employment Insurance, throughout the years, has been subjected to a flood of controversies [primarily surrounding the reforms made since 1971]
Although the bit in brackets adds some interesting details to the sentence, the sentence would work just fine without it. This clause is not essential, and so a comma is recommended.
If you remove primarily, it becomes essential, because we are taking exclusively about controversies surrounding the reforms made since 1971, so no comma is required:
Employment Insurance, throughout the years, has been subjected to a flood of controversies surrounding the reforms made since 1971
Note that this is a participial phrase, with surrounding as the participle. As this Purdue article states,
A participial phrase is set off with commas when it:
a) comes at the beginning of a sentence
b) interrupts a sentence as a nonessential element
c) comes at the end of a sentence and is separated from the word it modifies.
Following this advice, no comma is required because the phrase is not separated from the word it modifies (controversies).
For short adverbial phrases like throughout the years (this guide suggests three words), it is OK to omit the commas:
Employment Insurance throughout the years has been subjected to a flood of controversies, primarily surrounding the reforms made since 1971.