At WDW the "you can get a new fastpass at:" times are sometimes overstated. The actual minimum time window for a second fetch varied based on the fetch interval for the second ride.
For example:
Lets say I get a Splash FP and the re-fetch interval printed on the pass is 2 hours (2 hours later that it tells me I can get a new FP).
Then I go to the BTMRR FP distribution and the re-fetch interval is 1 hour (based on the 1 hour difference between current time and current FP return). I can get a FP for BTMRR 1 hour after my original Splash FP was issued (and an hour before the printed "you can get another FP at:" time).
Does
DisneyLand FP distribution work the same way?
I know the DLR FP system inside and out, and I know the WDW one pretty well too. But I am not sure I understand your question.
When you get a FP, there are four printed times. For example, see
http://hydroguy.smugmug.com/gallery/1738293#85956190-L-LB
1.
The distribution time - In the fine print at the bottom right is when the FP was distributed (11:01 in my screen cap above). That is unimportant
2.
The FP window opening - 11:40AM in my screen cap above
3.
The FP window closing - 12:40PM in my screen cap above (note that DLR does not pay attention to this time, only the window opening)
4.
The next time you can get another FP - 11:40AM in my screen cap above, where it says "Another FASTPASS ticket will be available after 11:40AM".
I think you are calling #4 the "second fetch" time. I call it the "Next Available FASTPASS Time". In any case, similar to WDW the "Next Available FASTPASS Time" (#4) may be the same as the window opening time (#2), or it may be sooner than #2 if #2 is more than two hours away from the distribution time, #1. If the window opening time (#2) is less than two hours, then #4 will always be the same as #2.
I noticed at WDW in some cases that the above was not always true. In some cases they would artificially delay #2, especially first thing in the morning. So on one morning I got my first FP of the day at Expedition Everest at about 9:15AM, and the window opening (#2) was 11:15AM. EE was down that morning due to mechanical problems and did not open until 11AM. The next available FP time (#4) on my EE FP said 10AM, which was
earlier than the #2 time of 11:15AM even though the #2 time was two hours away. DLR does not do this, and it confused me at first - but I just accepted it and it worked fine.
Also, WDW always seems to add 5 minutes to your next FP time (#4). Thus at WDW when the FP says you can get your next FP at 11:05AM, you can in fact get it five miniutes earlier at 11AM. DLR does not do this. If it says 11:05AM, it means 11:05AM.
MK always has their first FP return times (#2) one hour after the park opens, while the other WDW parks have theirs 40-45 minutes after. At DLR the first FP return time is always 40-45 minutes after the parks open.
So, I am not at all sure I answered your question. But I hope this helps.
FWIW, the DLR FP system has a number of tricks that do not exist at WDW. This link discusses them all:
"The Joy of FASTPASS - details and secrets"
www.micechat.com/forums/showthread.php?t=5720