Imagine the situation where the PCs are caught tampering with technology by a member of the Adeptus Mechanicus, let's say a Techpriest. The tampering part could be like just not saying the proper rites of using technology or perhaps slightly misusing technology for a different purpose. I know that every npc will react differently, but what would the "proper" stance be of someone of the Admech. A wristslap? Or would they call the Adeptus Arbites so to speak?

There are obviously many ways to deal with such a crime.

The mechanicus will try the heretics themselves. They are a religious order and religious nuts people like to keep punishment options under their own thumb (see every religion ever). So no arbites required. And any tech-priest will have mechandrites, servo-skulls and attending servitors to help enforce his judgment. Or he can easily get such assistance if necessary. If any PC even thinks of defying the tech-priests as they tend to be pretty nasty about withholding support.

Punishment must fit the crime but punishment in 40k always errs on the side of being ridiculously over the top. So depending on the actual crime, it can range from having to recite the proper hymns and procedures or be lashed, having one’s cyber-replacement turned off for a set period, be sent to a compulsory refresher course to relearn the proper hymns and procedures, defend oneself before a board, tribunal or a logis-temple asking the questions….And finally, there is the option of being turned into a servitor for abusing the machine spirit.

If it is minor, I'd go with rehabilitation and/or time in some sweltering factory. If it's major, servitor parts is a risk.

If it's minor the techpriest may become adversarial and make it harder for them to acquire tech for a while. If it's severe the Ordo Juros gets involved and well, they aren't a kind bunch of cog-boys. Just make sure whatever it is you do is way over the top cause it's 40k.