The past perfect tense is used to say that an action is completed before a point of time in the past and after the main action is completed. In this sentence " I recognized her at once" is the point of time in the past but after the action 'seen' Therefore, this sentence has a correct meaning.
Originally Posted by simile
compare: My father had built our house before I was born.
When two actions take place together in the past, both verbs are given in the past tense.
I recognized the girl at once when I saw her.' In this sentence the main verb 'recognized' and 'saw' happened at the same time. This is a simple past tense construction.