I agree that the lower matrix number is not always the A side, but in this case, we also have an Imperial ad that lists "Hide Away Blues" first, then "She's My Baby." That seems to prove beyond all doubt that Imperial was pushing "Hide Away Blues" as the A side.
fatsfan is correct in placing "She's My Baby" as the "A" side. It is a common practice for these sites to automatically list the lower master as the "A" side. All Imperials and many other labels have have real master numbers as used in the sessions, which means that the number is no indication as to the intended "A" & "B" sides.
This assumption started in the UK for labels like London which assigned their own matrix numbers, also known as control numbers. This is correct for many of them but if London took more than 2 numbers at once, often for an LP or EP, a number would be assigned for each track even though they weren't shown.
Example would be Jerry Lee Lewis' where "Mean Woman Blues" has the lower number but the flip was beyond doubt always intended as the "A" side ("Great Balls Of Fire"). This happened because Sun had already sent the 4 tracks for his first EP which London didn't release but used 2 sides for flips. Several Fats couplings were also swapped around in a similar way.
Recorded December 10th, 1949
Fats 4th recording from his 1st session (IM-135).
a-side of Imperial 5077 b/w "Hide Away Blues".
J and M Studio, 838 North Rampart St., New Orleans, LA
Released: May 1950
"She's My Baby" was a local seller, but didn't hit the national R&B-charts.
Antoine Domino(v/p), Dave Bartholomew(tp), Joe Harris(as), Clarence Hall(ts), Herb Hardesty(ts), Alvin "Red" Tyler(bs), Ernest McLean(g), Frank Fields(b), Earl Palmer(d).
Producer: Dave Bartholomew
Engineer: Cosimo Matassa
Recorded December 10th, 1949
Fats 3rd recording from his 1st session (IM-134).
b-side of "She's My Baby" on Imperial 5077.
J and M Studio, 838 North Rampart St., New Orleans, LA
Released May 1950
Antoine Domino(v/p), Dave Bartholomew(tp), Joe Harris(as), Clarence Hall(ts), Herb Hardesty(ts), Alvin "Red" Tyler(bs), Ernest McLean(g), Frank Fields(b), Earl Palmer(d).
Producer: Dave Bartholomew
Engineer: Cosimo Matassa