Player positions will be set (locked) at the start of your contest's draft for Head-2-Head and will stay in that position for the duration of the contest.
If a player's position changes after the draft's initiation, only new contests will have the player's new position.
For Tournament style contests, players are locked in at their position and per-game cost the moment the contest is created.
Player positions and availability for a contest are set and locked at the time of the draft or contest creation.
What does this mean for your contests and rosters?
If an MLB player is set as a DH for his team when your draft begins, he will remain as a DH for the entirety of your contest, even if he is moved from DH to 3B, he will always remain in your DH roster position. This would be the same for NBA players who may move between the Center and Power Forward positions.
When your draft begins, the only available players will be players signed to a contract and with their teams' active roster. This means that any player at the time of the draft or contest creation who is assigned to or with an affiliate team, will not be available for the draft, or to be added to your roster at a later time if they are called up.
For example, MLB or NHL players who are called up from their farm teams. NFL players moved from the practice squad to the active team roster. Players who are unsigned at the time of your draft or contest creation but sign a contract later that week.
All of these moves will not make those players available to be added through swaps or waivers during a contest.
Note: The ability to add previously dropped players back into you lineups is only available within SuperFlex DFS and Prime Time Flex contests.