We're old fashioned and believe in discrete agreements for discrete purposes. Because of that, we see three agreements in your future
Managing the band. You'd use a management agreement with the band. Because you seem particularly interested in the career of the lead singer, you would probably want a leaving member provision that allows you to manage any band member who strikes out on their own.
Music publishing agreement. Traditionally, when a manager wants a cut of a musician's songwriting income, the manager acts as music publisher and enters into an agreement with the songwriter, either a music publishing agreement or music administration agreement. In the music publishing agreement, the music publisher acquires copyright in the songs and the songwriter gets a cut of revenue. In the administration arrangement, the songwriter retains copyright and the publisher gets a cut for handling the paperwork associated with song promotion. As a general rule, we discourage musicians from entering into publishing agreements with managers unless there are strict limitations on time (it should not extend much longer than the management deal) and songs (it should only cover songs released during the management term).
The tribute band agreement. Why are you getting paid by the tribute act? If it's because you're booking shows, you would use a booking agent agreement. (Note, that in some states, like California, booking agents are regulated and must be licensed.) If it's because you're managing the act, then you'd use a management agreement.
FYI Dept. You can find detailed explanations of all three of these agreements in our book, Music Law, or in our exciting new Music Law program presented by Lynda.com