Qualtrics will tend to avoid sending a duplicate message to the same person if the individuals are in multiple segments, receiving the same message and inviting them to the same survey but on a timed stagger.

However, if the different segments are receiving different messages (A/B message testing, etc) or you need the groups to be the same size, then I would suggest that you set each successive segment definition to include a clause that the contents NOT include anyone in the prior segment(s). 
Eg Segment 2 excludes Segment 1, Segment 3 excludes Segments 1 & 2, and so on.

I tend to default to adding the criteria, just to be certain of the behavior (because sometimes technololgy gets updated and specs change), but I understand that’s tiresome when your list is large and there will be many segments.

I agree with @CarolK to have the most control and know exactly who got what being explicit to exclude people in prior segments is best. Qualtrics Directory has a nice feature where you can set conditions on “Mailing List” and pick your list/sample to exclude or include. I can see how writing exclusions could get tedious when you are 10+ samples in and need to hand code each of these into the sample exclusions.

If you can, I recommend using Excel or another external product to assign an embedded variable that can be used to create the sample. I’ve often used rand() functions and pivot tables to see that I’ve hit my sampling criteria when splitting a large file into smaller samples.