Based on the rulebook context, ties for objectives are resolved independently for each round, and scoring is "friendly." This means:

• In the round where the tie occurs, all players tied for first place place their markers on the "1st place" space and gain the full VP for first place. The next player places their marker on the "2nd place" space, and so on (Page 14).
• In subsequent rounds, the scoring is determined solely by the number of items specified by the objective for that round. If a player has fewer items than others in later rounds, they will score according to their position relative to other players for that specific round's objective (Page 14).

Each round's scoring is independent, so a tie in one round does not affect scoring in later rounds.

Summary

If a player ties for first place in one round but has fewer items specified by the objective in subsequent rounds, they will score based on their position in those later rounds without any carryover effect from the earlier tie.

Source: Wyrmspan Rulebook (pp. 14, 15, 2, 6)