As has been mentioned by others, buddhism among chinese, has been mixed with taoism, confucianism, moism, animism, ancestral worship etc. Contrary to popular msian belief, only a small number of chinese are practising buddhist, while majority of chinese here are taoist. They are only buddhist on paper because our government punya stupid forms only recognise buddhism as religion (when in fact it is not) but refuse to acknowledge the existence of taoism.
The ritual of burning of effigies, offerings and etc are all NOT buddhism, just to be clear. buddhism principles advises followers to accept that death is natural, and for surviving members to live and let go. However the practise of ancestral worship, paying respects to the departed is a deeply entrenched cultural practise for the chinese, long before buddhism even reaches china.
One may choose to follow strictly to the knowledge and practise of a devout buddhist, or one may choose not to. After all if one is not a buddhist, why must one subscribe to buddhist principles anyway?
However this is the beauty of buddhism, that is, you are free to choose your way. What Lord Buddha left for us is his knowledge and understanding of the subject matter called enlightenment. He has merely lay down a guide to achieve our own enlightenment and freedom from samsara, freedom from suffering and freedom from cycle of death and rebirth. He does not rule over your life, neither rewarding you for your obedience nor condemn you to hell if you turn your back on him (or his teaching).
Hence due to the liberal attitude of buddhism, it is no surprise that in the course of spreading the knowledge, there are bound to be teachers who would modify come contexts to suit the local populace where the knowledge of buddhism are taught, and hence today you see plenty of variations, and different forms of buddhism around the world. Theravadin, mahayana, tibetan, zen, new age etc. they may differ in terms of practises, rituals, rites, and some even propagated to the realm of mysticism and religionism, however the most basic reason of buddhism remains the same, and that is for deliverance and freedom from samsara.
Hence, whether rebirth is immediate, 3 days,7 days , 100 days or whatever, does it matter? The basic understanding is that death and rebirth occured. And because of death, it caused pain and suffering to the remaining family members and friends. And rebirth occured, because one has yet to achieve enlightenment, due to attachment to cling to life, or to be dragged down by own bad karmas of past. Hence when we are still alive and we have a concious mind, we are provided with the best opportunity and environment to seek and understand dharma (buddhist teachings), to judge and learn, and to make concious decisions that will lead to enlightenment and freedom.