~~~ 'reassembly' providing the glass fits in an up-close position against the chip and its repositioned inlay as it did prior to you removing it from the frame. It also sounds like the inlay would have a kind of locking-in, built-in device (the fragment of core composition on the back of the inlay) which could help in the positioning of the inlay -- where possibly no glue would be needed which might casuse an unsightly effect if too much is used; oosing out on the edge under pressure.

I've heard of this happening on frames (and in flips), before, but in most cases it was learned that the chip warped causing the inlay to pop.