Aashpreet, 

The action ( arriver) in the subjunctive clause follows (in time) the action in the second clause (partir) in this example, therefore the subjunctive verb will be in present subjunctive form (in modern French usage). 

The present subjunctive is the most commonly used form of the subjunctive. 

Only if an action in a subjunctive clause precedes an action in the principal clause would past subjunctive be used - the indication of ‘ antériorité ‘.

The attached is quite a good link on ‘ la concordance des temps ‘ which is in play here, and is strictly adhered to in French, somewhat less so in English nowadays. The discussion on concordance with the subjunctive reflects modern usage, that is with only 2 subjunctive tenses in use - present and past. 

Cécile wrote an answer recently on ‘ concordance des temps ‘, not specific to subjunctive, but covering the important rules. I can’t find it to link, but hopefully she or Céline will be able to recover it.

https://www.francaisavecpierre.com/concordance-des-temps/

The past subjunctive is also used to stress the completion of an action, It could be translated as "by the time we had arrived". It makes more sense with a verb which takes time, for example distinguishing between "by the time we ate" and "by the time we had eaten". In the case of arriver it's unnecessary, but I don't think it would be incorrect.

Thank you for you kind response Maarten and Alan!