Biggest thing with rebuilt or new or even old pump is to make sure it does not run dry even for seconds when first filling it up. I have seen them score pump body to make noise forever by simply being slow to get more oil in there. As little as five seconds dry can score the pump if the parts scrape off oil to be dry. I always stand over the reservoir and have someone else crank the motor, that way I lose no time chasing the reservoir level, a good working system can void all oil in it in like ten seconds or less.
If old pump not making noise I wouldn't change it, the hose could've been ready to blow anyway. You NEVER hold power steering on the limit for more than a second, and risking things doing that, the pump ramps up to full output and the bypass (your 'bleed off') bumps open trying to save pump and lines. Sometimes it can't do it............ ..the systems are not supposed to be abused like that.