So does the ATTiny device pull down SDA line to ack the write command or not? When addressed with write to its I2C address, most slave should pull down SDA bus to ACK master. If it always not detect that ACK, then there is something wrong.
https://my.st.com/public/STe2ecommunities/ImageLibrary/STM%20I2C/i2c_waveform_correct.jpg
Please see that picture showing the ACK