That deer couldn't have been down for 15 minutes before that yote showed up.
Simply, coincidence! It can take a coyote, or coyotes, several days sometimes to find a dead critter, of any kind. It depends on a bunch of things as to how soon they find it, UNLESS there is a constant food supply, such as a dead pile where farmers throw thier dead critters all the time, and then you can expect a coyote, or coyotes, to visit that spot daily!