Aussitôt introduces two actions, of which the first one has already completed before the second one starts. Since both actions happened in the past, the first one requires the plus-que-parfait (étions arrivés).

Andy, 

As Chris notes, the tense used is plus-que-parfait parfait, which conveys the order of the events being discussed here. 

I think it is better to start from the likelihood that the tense used in French by the native French writer, and speaker, is ‘ correct ‘ - only rarely will it be otherwise, especially on this site with the staff having professional qualifications. From that assumption, when uncertain, I try to understand what the tense they have chosen tells me, compared to any alternative I think may be possible. 

There are situations in which there is a choice of tense depending on the message to be conveyed. Although it discusses imparfait and passé composé, the attached link is one of the most practical discussions I have come across on the use of these 2 tenses. It helped me develop a ‘feel’ for them, and understand that the choice is not always set in concrete !

https://www.frenchtoday.com/blog/french-verb-conjugation/passe-compose-versus-imparfait/