ipod 4th generation

While the technician may have synchronised the two devices, he/she did so without iTunes. And therein lies the problem.

As stated, iTunes cannot put music from an iPod into iTunes. So if you no longer have the original iTunes Library with your music on it, your only option will be to use thrid-party software to recover the music from the iPod. See this tip from user turningtest2 on how to do this: Recover your iTunes library from your iPo… - Apple Community.

Some of the programmes he suggests are paid-for applications.

I think this depends on what you have done up to now.

How did you manage this transfer because there is no native method for transferring or copying from one iPod to another?

The correct method to get the same music onto a different iPod is to synchronise the music from the original iTunes Library that was used for the first iPod. If you no longer have the original computer, you should have copied the music from the old computer to your current one and then created a new iTunes Library on it.