Michael E. McLaughlin, who abruptly resigned as Chelsea housing director last month after his $360,000 salary was revealed, put in only 15 full workdays in Chelsea all year to earn his extraordinary paycheck, according to a Globe review of his work cellphone records. The phone records are like a diary of McLaughlin’s work life, painting a picture of an executive who was constantly on the phone but rarely stayed long in the city where he managed low income housing.