A couple of points:
- Buddhism/The Buddha/Buddhists never claimed that there is no such thing as self. The Buddha’s own quest for nihilism of self was a failure from where the middle path arose. Hence the idea was that, there is no ‘separate self’ that stands apart in isolation but is part of a larger consciousness. There is no disconnected self is not the same as “there is NO SUCH THING” as self.
- Mindfulness does not stand apart as well. It is integral to The Buddha’s eightfold path to the state of end of suffering. So mindfulness is a combination of “samma sati” (right remembrance), and “samma samadhi” (right concentration), but is part of a package: simultaneous or coexisting other practices of right speech, thought, action, livelihood. You have no way of isolating “mindfulness” effects from the combination of everything else, so a notion of “why mindfulness works” is pointless, really.