Although it has been sometime since I did my WES, I will try and recollect the process.
For studies in India, WES says only for autonomous colleges attestation from college principal will be accepted, otherwise one needs to get attestation from either the registrar of the university or the controller of examinations. These are central positions of the university (and not college). So for colleges that are listed under the non-autonomous list of WES this is the process to follow. I highly recommend not to take chances with what the recommendation is from WES. In developed countries there is a very high amount of trust on the process and on paper documents. Deviation from the process might cause unnecessary delays.
If you have studied abroad, like in USA etc. then your institution can directly send your transcripts to WES once you have made the request and necessary payments to your institute abroad. So essentially different countries have a slightly different process, as per WES. Just follow the instruction on their (WES) website. Hope that clarifies! Thanks.