Answer

Based on the rulebook context:

• Each Investigator takes their turn in full, one at a time, within a round (page 7).
• During their turn, an Investigator may perform any number of Actions, including Interact to pick up a token such as Evidence or a Point of Interest (page 8).
• There is no simultaneous action; Investigators act sequentially, not at the same time.

Token Acquisition

• If multiple Investigators wish to interact with the same token in a round, the first Investigator to take their turn and perform the Interact Action on that token will acquire it.
• Once a token (such as Evidence or a Point of Interest) is picked up by an Investigator, it is no longer available for others to interact with during that round.

Timing Conflicts

• There are no timing conflicts to resolve because turn order is sequential and determined by the Investigators themselves each round (page 7).
• The Investigators may discuss and decide among themselves who will act first, but once a token is taken, it cannot be taken again.

Supporting References

• "The Investigator players may take their turns in any order within each round. Each Investigator takes their turn in full..." (page 7)
• "Any number of times, you may do any/all of the following, in any order, based on your location, even while Moving! On your current space: Pick up a Point of Interest or Item token. ... Pick up an Evidence token..." (page 8)

Summary

The first Investigator to interact with a token during their turn acquires it. There are no timing conflicts because turns are taken one at a time, and tokens are removed from the board as soon as they are picked up.

Source: pages 7–8

Source: Core Rules (pp. 14, 16, 6, 7, 8)