These districts and sub-districts are so confusing, i can never work it out. I get registration and ecclesiastical districts confused, oh and guess what, there is a third Pump st on the Manchester NE map!
As far as I have been able to work out from census and certs of my own, the St George registration district is the bit we've been talking about, between Oldham Rd and Rochdale Rd. I never heard of "St George" district when I was actually living in Manchester - just thought of that area as part of Ancoats, on the border with Collyhurst. So I think your Pump St is the one you first thought of, between Oldham & Rochdale Rd.
The Pump St by Osborne st is near St Patricks RC church on Livesey St, and I would call that area part of Miles Platting myself.
The third Pump St is tiny and is in the New Cross/Holt Town area at the Beswick end of Ancoats.
And looking at Viktoria's Back Pump St on a later map (isn't on the 1891) it doesn't seem to be at the back of any of them!

Its at the back of Naylor St and Gunson St.
If we can find the Raticans in 1891 really, might settle the matter one way or the other...

Barbara