I've been working in a cafe since I was a freshman.
means that you started working at the cafe when you were a freshmen. It doesn't say if you started near the beginning of your time as a freshman, near the end, or in between. This sentence also, as a comment points out, implies that you are no longer a freshman, but says nothing about how long ago you were.
I haven't seen him since I lived in London.
means that you saw him while you lived in London, but not at a later time. so your "not seeing him" started while you lived in London. I don;'t think this sentence really implies anything about how frequently you saw "him" while in London.
I've exercised regularly since I lived in London.
probably means that you started exercising while you lived in London and have ever since. But it could be used to mean that you started just after you left London. That second meanig woulod perhaps more likely be expressed by somethign like:
I've exercised regularly ever since I left London.