Master Read Mode means that the slave has to transmit data to the master. Data is read from the transmit buffer and stored into the USI data register.
When the byte has been shifted out successfully, the slave listens for an ACK from the master. A NACK from the master is interpreted as the end of the message, and tags the transmission buffer as empty before resetting the interface.
When getting an ACK the next data byte in the buffer is put in the USI data register for transmission. Etc.