Is it a good thing if an employer wants you to call them after a job interview in a couple of days or would they call you?

Consider it a test. If I was an employer, and asked you to do something, but you didn't do it, I'd eliminate you.

Normally, it's the applicant's responsibility to follow up via phone, email, or letter, within a few days.

It depends on the company and it saves them money if you ( and everyone else they interview ) are calling them

That's an odd request of an employer, but maybe he/she is odd. Normally an employer calls you if they are interested.