Wiring doesn't have any sort of delay (except for logic gate stages, but that doesn't matter here). I'll try to give a play-by-play, hopefully, this will clear things up.
First of all, Terraria keeps a list of at most 1000 "mechs", which are essential timers. These keep track of cooldown times for things like dart traps, but timers also use them to activate a wire signal periodically. When a normal trap like mech runs out of time, it just gets removed from the list, but timers instead emit a signal, and then reset their time, always to 18000 frames. (Which then gets divided to form the various different kinds of timer delays.)
So, here's what happens when two timers are connected together, and you turn one on manually:
- T1 gets added to the mech list with 18000 frames left.
- Some time passes, the game keeps updating mechs, decrementing their time, until T1 gets sufficiently low to trigger on the next update.
- The game once again starts looking at the list of mechs, in order.
- Once it reaches T1, it decrements the time, and sees that it should trigger right now, so it does.
- Wire triggers always ignore the tile(s) that started them, so T1 is unaffected by this.
- T2 turn on, it is added to mechs for triggering later, with a time of 18000, but importantly, it will be placed into the list after T1.
- The mech time value for T1 is reset to 18000.
- The game continues updating mechs, still during the same frame, and eventually comes upon T2
- T2 is not ready to trigger, but it's frame time is decreased to 17999.
- At this point, T2 has less time left than T1, so the next timer to trigger will be T2.
- Time passes, updates happen.
- Time is up for T2, it gets triggered, trips the wire, turns T1 off.
- Time for T2 is reset to 18000.
- Repeat from point 2, but switch "T1" and "T2" around.
So, basically, the point is, a timer, activated by a another timer with the same length, will always trigger before the timer that activated it. If they are connected, the second timer will turn off the first one, before the first one has a chance to activate.