"Worrying" in the phrase you cite is a gerund, not a present participle. A gerund is a verbal noun. A present participle is used, along with a helping verb, to form certain verb tenses. So, for example, "I am worrying," "You were worrying," "They had been worrying," etc.
So, how do I know "worrying" is a noun (and therefore a gerund) in this phrase? Because it is the object of a preposition ("without"). You've got a prepositional phrase: "without worrying," so "worrying" must be a noun, and since it's a noun, it must be a gerund, not a participle.
Hope that makes sense. I'm new around here!
PS: I just realized, I did not address your real question, about how "worrying" could be modified by an adverb if it is a gerund rather than a participle. The rule you cite does not seem right to me. Worrying excessively. Swimming quickly. Eating heartily. These all seem fine to me. The thing to bear in mind is that gerunds are verbal nouns, meaning they are nouns, but they are related in form and meaning to verbs, and they share certain qualities with verbs. One of their verbal qualities is that they can be modified by adverbs.