I'm noticing that every now and then I see people in the database who should be members of engagement programs but aren't. The reason seems to be that if I use the trigger 'Person is created' and there are other filter criteria in the Smart List, the trigger has done it's job, but maybe some of the filters being used aren't set yet (for example, I might set a Region value in another program - e.g. 'United States'). so by the time the Region value has been applied, the time that the trigger is operating in and checking the filters has passed...I know someone advised using the 'Campaign is requested' trigger instead, but to be honest I've never seen a clear definition of exactly what that trigger is supposed to do...
For Engagements, the cadences are "regular", that is, they are on a set schedule for Mondays at 3pm, etc.
So there is NEVER a reason to use a trigger unless you happen to need an immediate emails send before the Engagement's emails. Thus, you should setup a batch campaign to capture everyone who meets the Entry criteria that day (or week). This will solve your problem by picking up those who qualify, when they qualify and avoid the point in time trigger issue.