They pay for development, they get branding, but for how long?
The answer might change your thinking. Exclusively theirs forever, less attractive. Exclusively theirs for a year, then no restrictions on what you do next, more attractive. Theirs for 3 years, then you can take it to others who are not their competitors, perhaps less attractive.
Six months' exclusivity? Without knowing any other details, this sounds great to me. You get to build something, it is theirs alone for six months, and after that, well...
...were it possible for others to learn what your were doing, perhaps they would sign up quickly on the first day of the seventh month....
The answer might change your thinking. Exclusively theirs forever, less attractive. Exclusively theirs for a year, then no restrictions on what you do next, more attractive. Theirs for 3 years, then you can take it to others who are not their competitors, perhaps less attractive.
It's all in the details.