I would like to know if we need a transit visa for China from Philippines

Mari, the rules are quite clear regarding 24 hour visa free transit and your itinerary within China, if less than 24 hours long, would not need any kind of visa. Anyway, having all those recent first hand experiences in mind with Philippine airport authorities who have presented themselves as ignorant folk by not allowing boarding to people who clearly have every right to be boarded, I really cannot tell you not to obtain a Chinese transit visa, especially because you have two stops in China. To conclude, your itinerary is eligible for 24 hour visa free transit, but I'm afraid that the Philippine authorities will not allow you to board the plane because of your two stops within China. Weird, but this is what are they doing. It would be a bit better if your entire itinerary is on China Southern. In this case, you would be almost certainly allowed to board the plane, but I cannot be so brave to tell you even in this case not to obtain a Chinese visa in advance.

Now, you know... You have right to travel visa free, but Manila airport staff will maybe invent their own way to interpret the rules and in that case, your money, time and health will be ruined. Now, it is up to you to decide.