Hi Thomas,
Maybe the new pump needed a little lubrication of the operating mechanism (I always lube new components before fitting) or perhaps there was a slight rough edge somewhere causing the diaphragm to stick initially? Once the engine has been run for a while, engine oil will have found it's way into the pump operating linkage. Has it been ok since?
From what you say, it seems that you have a pump that can be dismantled - v. interesting. I thought all modern replacement pumps were sealed units.
Talk of changing the internal spring, reminds me of when, back in the 1980's, I worked in a jet engine fuel equipment overhaul workshop.
One of the guys had a 126 which suffered from apparent fuel starvation when climbing hills. We dismantled the pump and found 1 or 2 coils had broken off from the compression spring. We had a spring tester, in house, and 'acquired' a suitable spring from our stores. Iirc it was stainless steel? Reassembled, the car went better than ever. Incidentally, I've often this type of spring failure on some other Fiat water-cooled engines, particularly the ohv 127 which I attributed to failure due to corrosion due to condensation damage.
Operating the pump and holding your finger over the inlet or outlet pipes is a common quick test of the operation of the internal valves. So I don't think what you experienced is unusual, providing the diaphragm returned to normal position when your finger was removed. If there is sufficient pressure in the pipe between pump and carb. the spring will be unable to move the diaphragm, so if you operate the mechanism, the diaphragm can't move? Or maybe I'm misunderstanding?
If you do dismantle the pump, it's important when reassembling that the diaphragm is not under any strain as this will add to the spring tension and possibly raise output pressure (maybe shorten the life of diaphragm also).
So, (IIRC!), the procedure is to assemble everything loosely, operate the pump as if you were trying to draw in fuel, tighten the screws on the body halves and then release the operating mechanism. This might not be necessary on all pumps, some have enough slack in the diaphragm or have a wavey shape on the moving section - you'll know when you start to reassemble the pump if e.g. the p.c.d. of the diaphragm holes is greater than the p.c.d. of the pump body, then you'll need to set it as above.
If you have the new (or old) pump apart, could you check the way it operates and report back. My previous post about pump operation was based on how a typical pump operates as described in a technical book, Fiat don't always do things the typical way
AL.