This sounds like a culture question that has meaning for some, but perhaps not as much for others.
Senior and junior have a few connotations, one that has to do with age, and another that is more based in seniority or title, such as in a business or perhaps even leaders of an organization, church or government.
In my experience, older people tend to be the ones who initiate any greeting, regardless of the age of the other. I suppose that's because they're not so inhibited by shyness or social moors anymore. The only exception to this I've seen is my granddaughter. She greets me even before I'm completely inside.
As far as the other goes, again, if a senior executive wants to greet a junior executive first, I don't have a problem with that either. It's obviously there prerogative, since they'd be in charge either way. In some schools of thought, treating subordinates like people rather than inferiors is a good thing. It fosters greater productivity, if the lines of responsibility remain intact.
So, in any sense of the terms, I'd be just fine with the senior person greeting the junior first.