I thought I posted a reply; weird
The copying happens in Step 2 of casting a spell. When the additional cost is paid, the embalmed spell becomes a copy of the creature selected.
So when you Eternal Servant the mummy bobcat, it will reanimate that bobcat and not the embalmed.
On summon effects happen the creature spell resolves and so they happen after step 4, which is why a mummy messenger's effect still happens.
Also the creatures school get's copied over. So a mummy messenger is holy. If that mummy messenger is destroyed, the creature does not change back to the embalmed. It would still count as a holy creature for triggering Gloranna's holy water sprinkler effect for example.