Arduino mini pro as ISP for Atmega329P-PU serial monitor failing
As you can see at image from linked instructables, they've connected TX pin from Tiny to TX pin on UNO through 220R resistor. This is extremely lousy idea as UNO and Tiny are both driving TX pins.

On the other side you've connected TX Output pin from Target CPU into RX Input of the Arduino ISP (pro mini). Arduino ISP returns some error responses from its TXO pin directly into the monitor. And it's at different speed I suppose, as default baud rate is 19200 in Arduino ISP sketch.

Also using internal 8MHz oscillator and: atmega328bb.build.f_cpu=16000000L means you are running at half speed as compiler and everything else expects. All speeds will be at half rate. Delays twice as long and so on.

Anyway, you can disconnect your USB to Serial converter and connect it directly to the target CPU. Or use two of them. Or just upload bootloader and get rid of ISP.