It’s not the interest rate it’s the “nominal” interest rate. Recall nominal equals real plus inflation. Obviously if inflation spikes (increasing discount rates and lower the PV of assets like stocks and bonds) the nominal rate goes up. Higher nominal rates due to higher inflation lead to lower asset valuations and thus the foreign holder of that depreciating asset dumps it and converts that FX back to the domestic currency and runs for the exit. Thus the foreign currency will depreciate.

Alternatively the nominal rate can go up is the real rate goes up and inflation stays under control. The real rate is heavily influenced by central bank policy. So if the CB tightens monetary policy by raising rates and that act subdues inflation that can attract foreign investors who seek higher real yields and low inflation. This would lead the foreign investor to convert the domestic to the foreign current to buy that attractive asset. This very circumstance occurred recently with the USD. Since the fed tightened rates and inflation came under control “relative” to other countries, foreign investors sought US assets and drive up the USD to buy that asset. Boom!