Reference tension set on the machine and string tension on the completed racket are related, but rarely the same. In most cases, if you ask for 56 pounds, the stringer will set that on the machine. Depending on the person, the method, and the string, the finished string tension will vary from that, dropping slowly over time. The 56 pounds you asked for is just a reference tension-- the amount of force applied to the string by the stringing machine. It doesn't mean that it's yielded the same finished tension when you had it done by other stringers.
The real question for you is: How does the racket play? If it feels the way you want it, you can use Racket Tune to measure future string jobs and have a reference for the finished tension you like. You can measure the finished tension, and, if it's not the tension you know you like, you can ask for higher or lower REFERENCE tension the next time you restring. You can also use Racket Tune after every hitting session to monitor the continuing drop in tension. At some point, you'll find the tension significantly lower than it was originally, AND you'll find the racket begins to play differently, forcing you to compensate with your swing. Tolerance for this varies from person to person, and it's generally better to tolerate less; you don't really want to continuously adjust your game. Once you've identified your tolerance, you can use Racket Tune to let you know when you're getting close, and can re-string... WELL before they break, for most players...
No way to know from this if your stringer is 'good' from a single sample. 'Good' really means 'reapeatable', so that your racket comes out the same every time it's re-strung. I'm sure your stringer is fine.
Here's a useful article: