When traveling, it's generally smart to pack in preparation for rain or any other conditions that may arise. The rainfall in Manila is roughly greater than that of Monterrey. You can assume this to be the case over the next 14 days.
Expect the weather to be around 36 °C on average in June. As the temperature peaks, try to get your plans done early, as flight price and availability will have an impact on your travels. The climate in Monterrey is generally hotter than in Manila.