Temporal Prime Directive. If it happened before they were fully formed (and at least on villain is from after that) than they cannot interfere with the course of historical events, as it already happened that way as far as DTI is concerned. Where they can interfere is if someone from their temporal line or associated lines of time interfere in events in the past (and possibly future).
As for the attempt to get around the problem by getting members from before the founding of the DTI, that would not be functional, as the farthest one forward would still be interfering with time and thus subject to the Timefleet dealing with it.
Thus you have agents messing with Archer's time because someone from their time (or at least their viable range) was messing with history. It is however possible to mess up on a temporal mission to correct problems (just as the Doctor in the TARDIS). So DTI and the Timefleet sort things out...more or less. They follow Starfleet precidents on time travel. The likes of Kirk, Picard, and Sisko all would fix things...more or less. Janeway mainly ran into Timefleet and Archer into agents and a Temporal Cold War. These agents and officers did try to fix things...in a Starfleet "more or less" kind of way.
As for the attempt to get around the problem by getting members from before the founding of the DTI, that would not be functional, as the farthest one forward would still be interfering with time and thus subject to the Timefleet dealing with it.
Thus you have agents messing with Archer's time because someone from their time (or at least their viable range) was messing with history. It is however possible to mess up on a temporal mission to correct problems (just as the Doctor in the TARDIS). So DTI and the Timefleet sort things out...more or less. They follow Starfleet precidents on time travel. The likes of Kirk, Picard, and Sisko all would fix things...more or less. Janeway mainly ran into Timefleet and Archer into agents and a Temporal Cold War. These agents and officers did try to fix things...in a Starfleet "more or less" kind of way.