I think half of the episode is the Tamarians genuinely struggling with human language. If the federations translation software wasn’t up to the task, it isn’t surprising that the Tamarian’s software wasn’t up for it either.

Based on the episode, it was prosibly the first time Tamarians ever had friendly and successful first contact. Because if they had it previously, they might have askee for help translating when meeting new races such as with the Federation.