Again, they take place at the same time, meaning you may do them in any order.
No they do not as destroying eveng doesnt happen at all. Tel trevura rule happens. It overrides the destruction rule.
If Tel would say "when you are destroyed instead" you would be right cause it would be:
-damage cards
-check hull
-destruction
-tel and DMS trigger
but there is no destruction step with current Tel wording.
But you have to deal all the cards that would destroy tel. At which point, it has no hull, and is destroyed. Tel's ability occurs after you have no hull. Which is also when dead man's switch occurs.
Tel's ability overrules the standard destroying ship rule. See Rules Reference, Golden Rules section.