Honestly that's what assassins do. They fuck up the carries and thats about it. However, some assassins have certain abilities that help them escape the team fights.
As an Ekko main, I usually try to set up my W stun and then go in and make a play. After I make my play and kill the carry or something like the carry, I instantly pop Zhonya's Hourglass, and the position of the enemy team determines my next move. If they don't move then I spam my ult button so any CC completely misses me when going from Hourglass to untargetable in my ult. If I manage to land my R and proc my passive then I can usually escape but if I dont get my movespeed from my passive then I have to rely on my team to finish the job, and without the enemy team's carry, it should be easy. If the enemy team backs up then I dont need to ult and I can save it for a later time. You should be building Hourglass on Diana anyway, and since she really has no escape, chances are she will die in the fight after getting 1 or 2 picks at the back line. Talon can jump over walls, so it shouldnt be a problem to escape a fight with him, especially when you have Mercurial Scimitar and a fast reaction speed.
For assassins you definitely want to know when their strong point is. For example, Ekko is his strongest when he has Lich Bane and Protobelt. Before then he is fairly weak and I need to play safe. Talon gets 60% or so of first bloods in games that he is played in due to his strong early burst potential and bleed passive. The bleeding paired with ignite is a ton of damage at levels 2-4. Diana is basically useless until she has her dash, so just play safe with her until then. Roaming is optional if you want to pick up assists or maybe some free kills but normally you want to farm up your lane to get to level 6 ASAP. Itll take a handful of games to determine the exact amount of damage you can do with your abilities and what to buy and such. There's a lot to think about when playing an assassin.
Talon is arguably the best midlane roamer in the game, so definitely prioritize that. Get Tiamat early and constantly shove wave and roam bot and, as long as you play it correctly, it's a free game.
I hope that was enough information. If you need anything else feel free to ask :P