This is exactly what I think Karma is not. A record? Where is this record kept? Who is keeping it? How does this record know how and when to extract its reward? How does your karmic record influence others to cooperate in its designs?
You got a theosophic reply. Here is a traditional theist hindu reply (though I am not one).
Karma is action/deed. A person's 'karma record' is kept in the office of the God of Death (Yama) who is the designated person to give rewards or punishment. Yama is helped in keeping the 'karma records' of all living beings (humans or animals, don't know about vegetation but most probably not) by an able accountant (Chitragupta) who is the originator of Kayastha caste of hindus.
The time and date of death of a person is decided in advance by Lord Brahma (Vidhata). At exactly that time and date, Yama makes his assistants (Yamadoota - Messengers of Lord Yama) bring back the soul of the living being. Chitragupta presents the beings record of karma, and according to standing instructions of Gods the person is awarded stay in heaven for his/her good deeds and hell for his/her evil deeds. These two are not compounded and have to be enjoyed or suffered separately, though the person has the choice to choose which one to be the first, heaven or hell.
The punishment or reward is irrespective of race, nationality, religion, sect, caste, etc. It is absolutely fair to all. To add some fun, Vidhata keeps the effect of some good or evil deed in abeyance, which is awarded in some future life without notice. That is why some people win lotteries (good deeds) or get involved in car accidents (evil deeds). Others are not involved in the affects of your karma. Those involved are paying for or reaping benefits of their own karma. For example, the driver of the car with which you met with an accident might be paying for his/her own bad deeds. But if the person is getting the reward of his/her good deeds, the car may not topple over in the accident.