The informal American-English phrase visiting fireman denotes:
– a person given especially cordial treatment while visiting an organisation or place;
– a tourist expected to spend freely.

The earliest occurrence that I have found of visiting fireman used in its literal sense is, in the plural, from the following paragraph published in The Sun (Baltimore, Maryland) of Monday 26^th November 1838—the Assistance Engine Company was one of the fire companies of Philadelphia:

The Visiting Firemen.—The papers in Washington and Philadelphia, announce the return of the companies belonging to the two cities, and the high gratification of the members. The Philadelphia Ledger says of the Assistance—“Some of the members appeared metamorphosed into Baltimore firemen, two or three of them wearing the equipments of the New Market Fire Company, and many of them the Patapsco and United Fire Companies.

Firemen’s visits came to frequently appear in the news. For example, in February 1911 only:
– in Massachusetts, “visiting firemen were present from many out of town places” at the fourteenth annual concert and ball of the Weymouth Firemen’s Relief Association;
– in New York, the exempt volunteer firemen of Kings County held the first annual reception and ball of the Flatbush Volunteer Firemen’s Association, attended by “a large number of visiting firemen from Queens, Nassau, Richmond and New York counties”;
– in Connecticut, “visiting firemen were present from Putnam, Dayville, Williamsville, Wauregan, Moosup and Jewett City” at the first annual concert and ball of the Danielson Firemen’s Association;
– in Vermont, “visiting firemen in uniform added considerable class” to the seventh annual ball of the Windsor Fire Department;
– in Massachusetts, “delegations of firemen from Boston, Hyde Park, Plymouth and Easton departments” attended the twenty-sixth annual ball of the Whitman Fire Department;
– in Louisiana, “visiting firemen” attended the seventy-fifth anniversary of the Baton Rouge Fire Department;
– in Kansas, “visiting firemen were present from all the nearby towns” at the fifteenth annual ball of the Coffeyville fire department;
– in Pennsylvania, the Wyoming Hose Company held their fair, “with the visiting firemen of Plymouth Companies No.1 and 2 in attendance”;
– in Connecticut, “visiting firemen from Worcester, Webster, Danielson and other places” attended the eleventh annual concert and ball of the Putnam Fire Department.

Welcoming visiting firemen became such an established practice that it was sarcastically included in a list of mayoral duties in One Mayor Turns Insurgent, an article about E. H. Lathrop, the Mayor of Springfield, Massachusetts, who had “pos-i-tive-ly re-fu-sed” to introduce Robert Edwin Peary (1856-1920), American explorer of the Arctic—article published in The Sun (Baltimore, Maryland) of Saturday 15^th January 1910:

Do the people elect a Mayor merely to run the city’s business and keep down the tax rate? Not much. A Mayor has more important duties than this to perform. He must help out at lectures, fill boxes at theatres, stand sermons, attend prizefights as a “fellow-member,” start off banquets, welcome the visiting firemen and take a turn with the Swiss bell-ringers.

The earliest figurative use of visiting fireman that I have found is, in the plural, from Cold Cash, published in the Watertown Daily Times (Watertown, New York) of Friday 24^th December 1909—Thomas Lee McClung (1870-1914) was the 22^nd Treasurer of the United States (1909-12), Charles H. Treat (1842-1910) was the 21^st Treasurer of the United States (1905-09)—“blayed” might be a misprint for “blamed”:

One billion, one hundred and seventy-five million dollars comprises about all the loose change Uncle Sam has at the present moment. Wherefore when Lee McClung receipted for it a few days ago, wrote his name at the bottom of a slip of paper reading like this: “Received from Charles H. Treat $1,175,000,000 in cash,” was he to be blayed—McClung I mean—for rising in his chair, carefully laying aside his pen for the McClung archives, and barking: “’Rah-’rah-’rah! ’Rah-’rah-’rah! ’Rah-’rah-’rah!” […]
[…] After the bills in circulation are retired, the name of Lee McClung will be found on every bill, national bank-notes and all—Lee McClung, treasurer of the United States—neatly engraved. It is a pleasant job and a comfortable one. All you have to do when you first get on the payroll is to practice writing your name on slips of paper until you get a classy signature, and then hand that paper to the man who runs the bureau of engraving and printing, where the paper money is made, who will see to it that said name is nicely engraved and put on the dies. After that you wait until the clerks count the cash on hand—that one billion, one hundred and seventy-five million—receipt for it, and then you are free for four years, or as long as you stay in office, to rest comfortably in a leather chair, and write occasional special passes for visiting firemen who come to town and want to see the treasury.

The second-earliest figurative use that I have found is, in the plural, from From the Snow-Clad Hills to the Beautiful Bermudas, recounting the voyage of a group of New Yorkers to Hamilton, capital of the British overseas territory of Bermuda, off the coast of North Carolina—story published in The Evening Star (Washington, D.C.) of Sunday 16^th January 1910; in the following passage, the tourists have just arrived at their hotel in Hamilton:

The immutability of British custom is here exemplified. It was New Year eve, and this steamerload of New Yorkers were intent upon celebrating it Broadway fashion. All went well until 11 o’clock struck—just the shank o’ the evenin’, when folks were beginning to acquire a thirst—when the local custom closed the bar. It was something awful the way those “visiting firemen” took on! There was wine behind the bar, money in their jeans, a frightful parching in their throats, but not for love or money, threats or cajolery, could another bottle be obtained.