Thrummingbird‘s ability triggers when it deals combat damage to a player. When this ability resolves you choose any number of permanents or players with at least one counter and add another counter of that type. Because this ability triggers when combat damage is dealt you can use the timing of when this ability resolves to your advantage.

Creatures with Infect will deal their combat damage to players in the form of poison counters. For example, lets say you are attacking a player without any poison counters with an infect creature and Thrummingbird. If both creatures deal damage to this defending player, this player will receive poison counters from the infect creature’s combat damage and you can have this player get one additional counter from Thrummingbird’s ability.