Oltec Matterweaver’s ability resolves before the spell that caused it to trigger. It resolves even if that spell is countered.

The new token copies the original characteristics of the target token as stated by the effect that created the target token and nothing else (unless that creature is copying something else; see below). It doesn’t copy whether the target token is tapped or untapped, whether it has any counters on it or Auras and Equipment attached to it, or any non-copy effects that have changed its power, toughness, types, color, and so on.

If the copied token has {X} in its mana cost, X is 0. (Most tokens don’t have a mana cost unless they’re copying something else.)

If the copied token is copying something else, then the new token enters the battlefield as whatever that token copied.

Any enters-the-battlefield abilities of the copied token will trigger when the token enters the battlefield. Any “as [this permanent] enters the battlefield” or “[this permanent] enters the battlefield with” abilities of the copied token will also work.