I am Oliver Lemke and I am working for the BMC Customer Support team supporting, among other products, the MainView Middleware Administrator (fka TrueSight Middleware Administrator) product. I will refer to the product as "MVMA".
Unfortunately we do not have any insight into how you would properly connect to MVMA so that the session cookie it creates when logging on gets preserved.
As the product is not doing unusual, maybe the POSTMAN Support team can assist you further. Or maybe there are even examples for logging on to web sites that are using session cookies.
As you got it working with curl, you see that you first generate the session cookie which you then reference on any subsequent actions you are performing against MVMA. I would guess that it is working very similar in POSTMAN.
Sorry for not having a better answer, but please understand that we cannot know the details of each third party product one can possibly use to exercise MVMA's REST API. Thanks!