I believe black can do no better than a draw from the starting position. First I'll give my own reasoning for it (and everything I'll say I've checked with Houdini, to rule out silly oversights on my part). Further below, I will suggest what I think is a very plausible explanation for why Chess Tempo's engine might have gotten it wrong.
The first move
1... Rb4
is forced, as it is the only way to keep white's b-pawn from queening without losing the rook. In turn, white's reply
2. Rb1
is forced, because without the b-pawn white will certainly be losing. Now white is threatening 3. b8=Q, which would force black to give up the rook. Since 2... Rxb1+ 3. Qxb1 doesn't help, black is thus forced to play
2... Qb6
Again white cannot let the b-pawn fall for nothing, and so has no choice but to play the sequence
3. Rxb4 Qxb4 4. Qa6
to stop black's threat of ...Qxb7. Now it is black to move from the following position:
[FEN "6k1/5p2/1Pp3pb/2q4p/1rNpPP2/3Q2PP/8/5RK1 b - - 0 1"]
[StartPly "9"]
1... Rxc4 2. b7 {Last given ply, white threatens b8=Q+} 2... Rb4 {First original move, prevent pawn promotion without loosing rook} 3. Rb1 {preserve pawn to avoid loosing}
3... Qb6 (3... Rxb1+?? 4. Qxb1 {pawn is just about promoted}) 4. Rxb4 Qxb4 5. Qa6 {black must now give perpetual check to avoid loosing}
Black would love to consolidate the position by getting the bishop to a spot where it eyes the b8 square along with black's queen (say by ...Bf8 followed by ...Bd6); doing so would eliminate any danger of white's pawn promoting, and allow black to regroup and win easily with the extra bishop. Unfortunately, if black tries 4... Bf8, then 5. Qa8 threatens to promote and simultaneously pins the bishop, preventing 5... Bd6. In that case, black has no better option than to play 5... Qe1+ and put white into perpetual check, draw. So 4... Bf8 doesn't work, but any other direct try by black to impede the advance of the b-pawn will just be slower. The problem is that, from the diagram position (meaning my diagram), black's forces are just uncoordinated enough that he doesn't have enough time to prevent Qa8 and promotion of the b-pawn directly, and must instead go in for perpetual check.
From a broad conceptual point of view, black has only one other idea to try and play for a win if he can't stop the b-pawn: to run his own d-pawn to promotion. But it's easy to see that that plan is also too slow. If black tries 4... d3, then after the white response 5. Qa8+ Kh7(g7) 6. b8=Q, black's queen is en prise and white is now threatening to mate. So black would again be forced to bail out and go for a perpetual check with 6... Qe1+.
What I think went wrong here
From your initial diagram position, an engine could search to a pretty healthy depth and keep seeing positions in which black retains a sizable material advantage (a full extra bishop). The reason for this is that though black cannot "really" stop the b-pawn from queening, he can give checks to push that event into the future, further down the engine's search. Now, of course, once an engine sees repetitions of the position in its search, it will recognize the draw and no longer see any advantage from the extra material. But ... (and this next part is indeed speculation, but it is not without sense)
A potentially problematic feature of this particular position, though, is that black doesn't just have, say, two checking squares from which the queen can carry out the perpetual. Checks can happen on e1, d2, d1, c2, c1, b2, b1 and in the meantime the white king could have at least 10 squares it could travel on; not to mention, a checking sequence could also get interrupted by, say, the white queen blocking a check, followed by the black queen getting back behind the b-pawn, and then the white queen returning to a6.
The point being, there are very many possible paths here; it's all still just a perpetual check, but the great variety of options here could make it so that, at whatever search depth it's working at in the Chess Tempo evaluation process, the engine couldn't quite see a repetition yet, because it keeps seeing things like, e.g. "Oh, I don't have to repeat with ...Qe1+, I'll check from d1 this time instead," pushing the recognition of a perpetual check beyond its horizon.
Again, I'm speculating, but it's at least not a nonsensical possibility.
1...Rb4 2.Rb1 Qb6 3.Rxb4 Qxb4 4.Qa6. However white's pawn is not really "disabled", just slowed down a bit, as far as I can see. How can black continue from there?