"After paddling out to her normal spot" is an adverbial phrase.
In a sentence, an adverbial phrase in the multi-word part which plays the role of the adverb. This means that it qualifies (gives the reader some information about) the sentence's main verb: how the action was done, when, where, etc.
Here, the sentence contains 2 main verbs: "paused" and "decided." They are qualified by the adverbial phrase "after paddling out to her normal spot" because this phrase is giving us details as to when the action took place.
Be careful not to mix up adverbial phrases with adverbial clauses. An adverbial clause is a multi-word part of a sentence which serves as an adverb but contains a subject and a verb.
