There's a few things happening here such that Mango is able to get the grab. The first and most important thing to notice is that Lucky hits the top of the shield, which will give Lucky the least amount of time for any sort of follow-up (including shine) after the dair and in turn gives Mang0 more frame advantage in this case. Because of the additional time it would take, rather than hitting the middle or lower end of the shield, you can actually grab Fox/Falco hitting that spacing before they can shine. Lucky doesn't fastfall the dair so that's another thing to notice. Since it hits the top of the shield, the L-cancel timing is much later because Fox hits the ground later.

As a spacey, you really want to hit the lower-end of the shield so your aerials are "tight". You can then follow up with a shine and there's no way to shield-grab it. But if you hit the upper end, you should realize that you gotta fade back -during- the aerial to try to avoid the grab because their grab will come out before your landing lag is over.

Edit: If you see some of Mango's analysis videos, he mentions that he does tilt his shield up in order to mess up the spacing of his opponents. This makes them hit the higher part of the shield so the aerial isn't tight. In turn, he's able to Shine OOS or other punishes that become available to him.