According to the web site's staff, Yevloyev arrived on the same plane as Ingushetian President Murat Zyazikov. After the president left, men from the bodyguard of the Ingushetian interior ministry surrounded Yevloyev, made him get into a car and drove him away.
According to the editors of the site, on the way from the airport Yevloyev was shot in the head, and then thrown out of the car. The seriously wounded man was found by his relatives, who had come to meet him. They took Yevloyev to hospital, where he later died.
Reuters has a report here.
RFE/RL has another Reuters report here.