Not only did Jason go over the limit of his data plan, but he also forgot to pay his cell phone bill on time.

In this sentence, what type of connection is the phrase "not only"?

In this sentence, the type of connection that the phrase "not only" represents is correlative connection.

Not only, accompanied by but also is a pair of correlative conjunctions. That means that two equal grammatical items are joined in one sentence. So this person did, or rather didn't do either of these things.