The frequency of the internal RC oscillator is only guaranteed to be calibrated from the factory within 10%, which is not generally close enough for reliable asynchronous serial communication. I haven't tried serial comm with an ATtiny84 myself, but I've found that many or even most of the ATmega328Ps I've tried are close enough. So it may just be bad luck but there are two options. (1) Change the clock source to an external crystal or resonator, or(2) Calibrate the internal RC oscillator (the datasheet says it can be calibrated within 1%).