We've got a fountain coming out of the top of the toilet's Siamp valve
when it refills. Is it new valve time, new part time, or is there an
adjustment to make?

The diaphragm, as far as I can see, is intact.

Image at https://flic.kr/p/2gSH4dP

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F

The flush button mechanism ought to be located in the hole I believe. I've not had occasion to strip one of those units but if a replacement valve isn't too expensive and considering plastic becomes brittle/prone to cracking,you might do well to just replace it. Others may be more familiar with the thing and offer a different solution.