Firstly, the panel is lightly cleaned to ensure any dust off of it which could have collected just after you bring it to them. They only do a light cleansing, you are accountable for ensuring that it is as clean as possible if you take it to them. Secondly, the bend tempered glass is sent via a machine which "super cleans" and dries it. Thirdly, the stained glass is further laid out on one sheet of the tempered glass. It can be centered and there's a gap on both sides and the top and the bottom of 5/16" (the dimension you subtracted from your completed dimension when making your panel). Fourthly, a sticky backed, foam tape with a metal skin is utilized towards the stained glass panel and the curved tempered glass below. It sticks to both pieces and holds them firmly. Fifthly, the metal tape is scored on every corner so it may be folded around the corner having a sharp clean edge. The tape can be different in width. Sixthly, laying the second sheet around the foam tape needs help because they only get a chance to process it perfectly. When the top sheet touches the tape, it is stuck. Because of that, it is best to often allow for an additional 1/8" within the completed opening of the door, if the two sheets are slightly misaligned. Finally, the completed "sandwich" of glass is clamped inside a table and hot butyl rubber is forced between the two sheets of tempered glass and filling the gap between these two sheets. This covers the foam tape entirely.
The bend tempered glass should be 1" smaller in size than the actual opening door when accurately sizes a window. Therefore, enough space is ensured for foam tape at the bottom of the opening for supporting the window as well as for silicone at the both sides and the top for holding the panel in a secure way.