I'm by no means an expert but I'll give it a go. So let's start simple with TIDI itself. It slows down time to give the server time to process everything. The percentage you see ingame is how fast time moves. At 90% 9 game minutes are 10 real minutes. At 80% 8 game is 10 real etc.

Most (all?) timers aren't affected by TIDI because there's no need. For a POS for example the defenders want to get the shield up to 50% and the attackers want to destroy the thing. The thing that makes citadels weird is the damage cap. Because the timer isn't affected by TIDI but your damage is i.e. you do less DPS (real seconds) in TIDI. So if you have just enough dps with no tidi you'll be fucked in something as little as 95% TIDI.

Let's say you do 100 dps with no TIDI. In 50% TIDI you'd only be doing 50 dps in real time. In gametime you'd still be doing 100 dps. But because the damage cap dps is in real time you'd have to bring twice the amount of ships. Now the obvious solution here would be to just have the timer be affected by TIDI as well but there's probably some technical reason CCP didn't do this. Possibly something to do with 10% TIDI still not being enough for the server to keep up and the timer getting weird. But I'm just guessing here. Aside from that it would also make the event much much longer.

The whole "achor at DT" tactic has a few reasons. First one being that it's generally the most quiet time in Eve. EU and US TZ is at work / school / sleeping and it's mostly kangaroos playing. Secondly there's a chance that something goes wrong with the server, as it did with PM's Keepstar. The game loaded on the server but because so many people were trying to get into the system it took a while for people to get back in. During this time the timer was still ticking down.