I had never heard the phrase "tarpaulin muster" before this Willie ad, myself, but it's popular enough a phrase to be the title of this 1907 book by John Masefield, which appears to be a collection of stories about the sea.
And according to Chapter Nine "A Tarpaulin Muster" from the book "My Union Right or Wrong, A history of the Ship Painters and Dockers Union 1900-1932 By Issy Wyner:
Aboard ship, when financial assistance was called for a distressed member of the crew, arising from an accident or other cause, each crew member was asked to place his contribution on the tarpaulin which covered the timber hatch covers enclosing the top of the ship’s hold. A crew member would stand by to remind the seamen of the need to make a contribution, and when completed the "tarpaulin muster" would be handed to the affected member or his family. In other industries, someone would take round the hat and, in later developments, someone would take up a list, with paper and pencil to record the names and amounts contributed.
And clearly what makes Willie a distressed member of the crew is the absence of alcohol. Oh Willie!