Multilingual large language models have emerged as a promising solution for resource-constrained settings, with significant efforts aimed towards improving multilingual capabilities of English-centric pretrained models. However, the broader cross-lingual implications of fine-tuning interventions remain understudied. This work examines instruction tuning (IT) over the BLOOMZ model for Question Answering (QA) in low-resource settings, with special emphasis on transfer dynamics across several languages. Our findings reveal two critical insights: first, IT on the target language can negatively impact its own performance in constrained short-span generation tasks due to overgeneration tendencies; second, in QA tasks, IT appears to suppress performance in some interfering languages, thereby enhancing capabilities in some target Indic languages by more than doubling QA performance. These results highlight important trade-offs in multilingual LLM adaptation and enhance our understanding of cross-lingual transfer mechanisms.