Answer

When replacing a Unit, the rulebook specifies the following sequence:

• "If you want to deploy a Unit on the same position as another card of yours, first you must destroy the card already in play that occupies that position, then you may put in play the new Unit. This is called Replacing."
  (Page 15, Section 4.4 - Replacing)

• "If the destroyed Unit has the Last Word attribute, you must resolve it before the new Unit enters into the battlefield."

• "The Unit that enters into the battlefield is actually deployed, thus it is exhausted and its Genesis attribute must be resolved (if any)."

Regarding when to pay the summoning cost:

• The summoning cost is paid when you put a card in play from your hand:
  "To put a card in play from your hand, you must pay the Essence Crystals required by its Summoning cost, indicated on the top-left corner of the card. After paying the card’s cost, place it on the battlefield..."
  (Page 14, Section 4.1 - Summoning)

Sequence of Actions When Replacing a Unit

1. Decide to deploy a new Unit (initiate Summoning, pay the cost).
2. Destroy the existing Unit in the chosen position.
3. Resolve the destroyed Unit's Last Word attribute (if any).
4. Deploy the new Unit (it enters exhausted, resolve Genesis if any).

Can you change your mind after seeing the Last Word effect?

• The rules do not state that you may change your mind after seeing the Last Word effect. The process is described as a sequence: you destroy the existing Unit (resolving Last Word), then deploy the new Unit (which you have already paid for).
• Since the summoning cost is paid before the card is placed on the battlefield, and the destruction (with Last Word) happens as part of the replacement process, there is no indication that you can reverse your decision after seeing the Last Word effect.

Summary

• You pay the summoning cost before destroying the existing Unit.
• You cannot change your mind after seeing the Last Word effect; the process is sequential and binding once initiated.

Source:
Page 14, Section 4.1 - Summoning
Page 15, Section 4.4 - Replacing

Source: Core Rulebook (pp. 14, 15, 22, 24, 26)