What does get ruined? The mold? The Result? Ive done a few pressmolds myself and I never had problems with separating. (But that's probably due to me letting them cure overnight.

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This is what I normally do with pressmolding:
1) Build a cage with lego and put the heated instant mold inside. This helps to avoid distending the mould.
2) Press the part inside with the goal to form a decent mold line. This often needs adustments to get a tight fit around the copied parts sides. Don't forget to add a few pokes with the backside of a brush or something. Those holes/bumps will help aling parts later.
3) Next add the other side of the mould with a lot of pressure, but try to keep it even. (Using a square shaped object helps in force distribution)
4) Most of the time the second side has the better detail coverage, so I simply redo the first side.
The resulting mould should be easy to remove and thanks to the bumps also easy to align. And the Instant mould is flexible enough to even allow some overhanging details. Its just hard to get putty into those areas. And better wait for the sape to fully cure or those details may still warp during removal.
If you fill in the mould don't fill it up completely. Too much putty results in massive mold lines, and often misalignments too. And fill both sides individually. Press the putty into each detail by hand to help coverage. Also pull it over the edges slighly, otherwise you might have holes along the sides. Only then press both parts together. You'll end with thin mold lines and additional putty will mostly be pushed inside the shape. Your result will probably be a bit hollow inside. But who cares as long as the surface is okay.
Another advice on milliput. Superfine is a bit tougher to work with. And due to its claylike consistancy will quickly stain your instant mould(All milliput types will probably do that). Standard milliput is cheaper and works better for Pressmolding in my experience. But the best results I had was with a mix of
GS and Milliput standard. Alternatively you could try and let the putty cure for a bit before adding it into the mould.
But despite all this, don't expect perfect results. With Instant mould press moulding you'll seldom get all the details propperly. But the results should at least be decent enough that it will look mostly fine once painted.
And I can't help you with resin dyeing. But are you supposed to add it to one side or during mixing of both sides? I always thoughs you add it during the mixing process and not before ...