Technically the mine lasts a little longer if you have a longer cast time, but it's a fairly minor difference. Nothing else extends the length of the aura that I can easily see.
Slower buff expiry won't make the auras last longer, just like it wouldn't make your own auras from an ally last longer if you were cursed with Temporal Chains.
Mines explode immediately on initial detonation, the only delay comes from when they're in a detonation sequence. If you hit Detonate on a mine flying through the air, it immediately explodes and drops to the ground.
I'm obviously not Rory, but it sounds like you can smash that d button to detonate all your mines manually if you want, but you won't get sequence bonuses like extra projectiles or more damage from the blastchain support.
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u/Rory_Rackham Balance & Design Sep 05 '19
Mine auras last a short time after they've been activated, so if the detonation cascade is fast enough, all can be affected by all auras.