With such replacement the bow should be checked, at the very minimum, for tune. Replacement strings and cables will never be exactly identical to what you had before so the bow's performance will be different. Your brace height, loop or nocking point, peep set-up, and any other string accessories will never be exactly identical. They may be very close, but never identical. For this reason the whole shooting system should be re-tuned so each and every one of the individual components are working together and in harmony with each other.
You said you had the bow tuned last year before the start of the season. With use a bow can go out of tune. Some of the mechanics of the bow can change and your individual shooting form may change over time. I believe it pays to learn how to tune your bow your self so you can stay on top of it's condition and performance. At the very least, learn how to recognize some of the critical components and adjustments. Record or memorize these and become very familiar with your bow, its components, and how it feels when you shoot it. That way, if something changes, you'll know it and can take the appropriate corrective action.
There's stuff on line about setting-up and tuning bows, and there are books available. Plus the fellows at your local pro shop should be willing to help you. Learn all you can about your tackle to get the most out of it. Asking questions like you did is a great beginning. Good luck to you.
The only after market strings I have got were from 60X. They were perfect and I am hard to please (so I've been told more than a few times).
What bow?
The reason shooting and THEN tuning is suggested is to let the strings and cables "settle in" to the bow and to let any string stretch or creep occur. Then when the bow components have adjusted themselves to each other and the string and cables have reached their final lengths, the bow can be tuned and the adjustments will hold for quite a while.
So, how much do do shoot prior to tuning? Opinions on this may vary somewhat but I would say at the minimum at least 100 arrows.
So, you put on a new string and shot it to get it stretched out. Then you had your bow tuned and the sight settings are different. Yes, it could be the peep is in a different location, and that may be the first thing I'd check. However, think about this for a minute,...the bow has a different string then it was tuned and all sorts of adjustments may have been made up to and including upper and lower limb tiller adjustments, arrow rest up & down and left & right adjustments, nocking point (or loop) adjustments, brace height adjustments, poundage adjustments, etc., etc. What I am saying is that you had the bow tuned and a great many alterations may have been made. It would be nice if after tuning our bows always shot the same, but oftentimes they do not. After tuning you hope they are reasonably close, but that is not always the case. I agree that now having to use a 37 yard sight setting for a 20 yard shot seems excessive, but when you consider all that was done this may not be a sign of trouble. Another thing to think about,...could it be that previously you bow was so far out of adjustment, that what is correct now actually seems to be incorrect? Who knows? But, if you bow is shooting well, if the arrows are flying true, grouping, and hitting where you aim, and if they are not fish tailing or porpoising, perhaps you should accept this "new" normal. If you still have doubts you could ask for a re-tune or take it to another pro-shop. Without actually seeing and shooting the bow, it is difficult to tell for certain what is or is not wrong with a bow. You might just want to give it a little time, see how it goes and enjoy the soon-to-be-here best two weeks of the fall hunting season. I wish you well and good luck in the woods this fall.