There are 2 ways to drip content in dap.

1) Day-based dripping
The users will receive access to content dripped on day X only if they are on the "Xth day or beyond" of their membership to that product.

So if you have content dripped day 10, a user will only receive access to it when they reach 10th day of membership.

2) Date based dripping
The users will receive access to it on the content drip start date only if their access_start_date to the product is on or before the content drip start date.
The user will lose access to it on the drip end-date or their access_end_date (whichever comes first).
You can find user's access start and end date to the product in dap users -> manage page.

So if you set content to drip with start date = 05/01/2012 and end date = 05/31/2012, then a user that joins in April can access content come May 1st.

A user who joins 04/30/2012 and has an access end date of say 06/30/2012, can access this content come 05/01/2012 and access it upto 05/31/2012 (because that's the content drip end date).

If a user joins 04/30/2012 and has an access end date of say 05/15/2012, then the user can access this content come 05/01/2012 and access it upto 05/15/2012 because that's when their access to product ends.

A user who joins 05/15/2012 and has an access end date of say 06/30/2012, can access this content come 05/15/2012 and access it upto 05/31/2012 (because that's the content drip end date).

NOTE: If you want them to keep access even after 05/31 or even after their access to product ends, then you must set "Allow access to previously paid for content" in DAP Setup > Config to "Yes".