This can be done in any number of ways depending on the country and the employer:
- The employer might tell you to get the university to mail them a sealed envelope with the transcript
- The employer might ask you to grant them guest/view access to your online student records (depending on the Student Information System at your university)
- The employer might ask you to send an electronically verified copy of the transcript (through a service like the National Student Clearinghouse in the U.S.)
- The employer might call the university and ask them to confirm particular information (e.g. the GPA and a couple of randomly selected grades -- this was what my former employer did)
- The employer might mail a copy of the transcript to the university as you suggested
In short, unless you know an employer's procedures, assume that they will find some way of verifying the information, either directly or with your help. Not complying with a request to verify the transcript after securing an offer (when a decent chunk of money is on the line) would look extremely suspicious and be grounds for withdrawing the offer in most jurisdictions.