"finally reaching" vs "finally reached"

I could get no further information from Mrs Fairfax about Mr Rochester, but instead she offered to show me round the whole house. We went through many large, impressive rooms, finally reaching the top floor, where there was a narrow corridor with several black doors, all shut.

Source: Jane Eyre (Graded Readers, printed by Oxford Press)

İs not the word “reaching” supposed to be “reached”??

We use the present continuous tense (ending -ing) of a verb to describe a shorter or temporary action that happened during another action, which can be expressed in the simple past, present, or future: I walked in the park, looking at the trees. Charlotte Brontë correctly used this.

Simple and continuous tenses