My understanding is that, in general, Broadway shows do not recoup from tours. My understanding is that, today at least, tours are separately financed with separate contracts. There may be an overlap of investors - so an investor in Millie, for example, may eventually make money if the tour is a financial success. But, if you were only an investor in Millie on Broadway, for example, you did not get all of your money back. There generally is no "mother company".
That said, the producers for the Broadway and Tour of Millie may have been the same - but not all investors are identified as "producers": (Also, the tour started in July 2003 - while Millie did not close on Broadway until June 2004)
IBDB lists the Broadway producers as Michael Leavitt, Fox Theatricals, Hal Luftig, Stewart F. Lane, James L. Nederlander, Independent Presenters Network,Libby Adler Mages, Mari Glick, Dori Berinstein, Jennifer Manocherian, Dramatic Forces (Dori Berinstein, Jennifer Manocherian, Peg McFeely Golden, Douglas Teitelbaum), John York Noble and Whoopi Goldberg; Associate Producer: Mike Isaacson, Kristin Caskeyand Clear Channel Entertainment
Ovrtur lists the producers for the tour as: Michael Leavitt.Fox Theatricals,Hal Luftig,Stewart F. Lane, James L. Nederlander, Independent Presenters Network,Libby Adler Mages, Mari Glick, Dori Berinstein,Jennifer Manocherian,Dramatic Forces, John York Noble,Whoopi Goldberg
Of course, each show's investment contract is separately negotiated and some may provide anciallary (souveniers, cast recordings) and tour income to the investors. Some may not. I have no idea what Millie's contract said. I tried to see if there was any information on Ken Davenport's website as to Broadway investors getting money from a tour, but didn't find a definitive answer.