"In a timely manner" is an idiom that just means something was done without wasting any time. They got the job done, or finished something, in a timely manner. They did it quickly. They were very prompt. If you said "Boy, you got here quickly.....in a timely manner".

Hi Nozturk it means to complete a given task in a reasonable amount of time. If I give you a book to read I'd appreciate it, if you read the book and returned it to me in a timely manner. (so I can finish reading it).