You have some weird builds, that would definitely be holding you back.
Beyond that, when facing an early game jungler, do you start top rather than bot, to ensure that they can't invade you? Your top laner won't miss xp or cs, and it doesn't take very long to clear your first buff, proceed to bot-buff, grab Krugs/Gromp, and then gank bot or mid. You'll hit 3, have both of your buffs, and the odds are that the enemy jungler will have proceeded to try and invade you, instead wasting their time before trying to gank top.
In a case of my most recent game, before 2:45 or so I had already taken my red buff, proceeded to blue buff and gromp, then was hiding in botlane brush with double buffs and lvl 3, arriving just as our botlane his lvl 2. I popped W on the enemy Twitch, Blitz and I flashed, we managed to insta kill their ADC and get firstblood.
All game our Zilean never used their wards (midlane Zilean), he was 2/12 at one point, he was constantly dying and feeding the Ahri. The enemy team was trying to rush out and shove our botlane, having warded our jungle, however they brought along no red wards, so I flanked and we managed to insta kill their carries, and picked up the win after wiping their group.
How are you positioning, other than the occasional bug (minions will sometimes randomly auto you while you are stealthed which reveals you), you can walk through the minions without worry. I don't recommend getting in sight range of the towers, unless you are sure no enemies can contest, instead covering your allies, if anyone walks into them they don't know if you are there or not, since at times you are there, and times you aren't, they are less likely to hard engage and contest the objective in question.
How are your backs? Don't be like the Xin Zhao from that match, he was 3/0/3, still had not backed, decided to 2 man dragon with Braum at like 8 minutes, instead they both nearly died, and he ended up having to give up a free infernal dragon to me and Zilean. He did this again later on with another dragon. How do you prioritize your objectives? Rift Herald is extremely easy to secure as Evelyn, her E does extremely high damage to it, even early, and she has good consistent damage to it. Evelyn is one of the few junglers that can easily and safely take Krugs early, receiving almost no damage from them if you kite them properly, so if I'm planning to lvl 3 gank botlane when I start on the 'bottom' team, they're not a bad idea to secure.
I see you with Stoneborn Pact, Colossus, I'm going to assume that those were accidents, as was the ardent censer, otherwise you have your answer already...
Don't take Abyssal Mask, don't take red smite, tracker's is almost always the best, don't take Rylai's second.
The most efficient build path is Runic Echoes, Lichbane, Banshee's Veil or Liandry's, Liandry's or Banshee's Veil, final item should probably be a rabbadons. Boots are a necessity, built to counter resists from your opponent, typically unless extremely AP cc or ap heavy team, you want tabis for the extra damage mitigation vs ADC's.
Why is this build the most efficient? Runic Echoes and Lichbane offer extremely high burst. Banshee's Veil is preferable as your next item as it helps when opening up on an opponent to avoid crucial incoming CC or ability damage, it might help prevent you from being revealed at some point as well. Banshee's offers MR, and gives high enough amounts of AP to be a viable slot choice. Liandry's is taken following that for better pen and helps you deal with tanks (your Q in particular becomes far more efficient with it), it also gives HP which helps offset the lack of sustain or survivability inherent in your kit (discounting the passive as that requires you to be out of combat and below a certain threshold for it to take effect). Rabbadons, and not Voidstaff is chosen as your final item, in particular b/c you don't struggle against Tanks, in part due to the choice of Liandry's (becomes far more efficient at killing tanks and squishies alike), but the E is where your tank killing talent really shines. It does high % max HP magic damage, and is empowered (and cd reset) if you stealth or are coming out from stealth, it deals more damage when empowered. It has a reasonable AP ratio, and therefore magic resist won't prove to be particularly difficult for you to overcome. You build Rabbadons for a final item due to it's lack of survivability (and as an assassin diving into the entire enemy team, it's an extremely risky item to take early which is why we focus mainly on items that grant resists or hp with AP over raw AP), though in theory you could build it earlier I wouldn't recommend it. If you are diving face first into tanks, you will not like playing Evelyn, as despite her high burst against tanks, you are still a squishy Assassin that will die instantly if out of position. She has no AD ratios, do not ever take Gunblade.
Her ratios require sizable AP amounts to properly scale, if you don't focus on building appropriate items to survive along with AP values in them (Liandry's, Zhonya's, Banshee's) you won't find much success. Rylai's is not a preferred item simply b/c it's not a particularly efficient choice for an Assassin, you have the benefit of positioning, over your enemy, and therefore have a massive advantage. Instead of Rylai's you could have had any number of items that offer significantly increased burst, or have a good passive (Liandry's, Banshee's, Lichbane, etc. you're losing something to build this item, and it's simply not worth it).
I legitimately 100 to 0 people all the time as Evelyn, she can quite easily abuse the enemy, especially the later the game goes, as the enemy has items in all 6 itemslots, they can no longer field redwards, they essentially have no idea where you are hiding at, and that's particularly troublesome for them if they initiate a fight w/o knowing where you are, or are otherwise out of position. Early to Mid game Evelyn is at her weakest, so you have to play far more intelligently than on most champions, she requires decent knowledge of her kit to properly make use of her, and you need to know how your enemy will react or respond to your decisions. Flanking an enemy, waiting until they are trying to poke at a weakened ally under tower, and then dropping your mark on them, they immediately begin to retreat, attempting to find where you are, but since they don't know where you are until the charm is proc'd, they will most likely run towards their tower or teammates, in particular, you can abuse this by choosing to pop the charm soon, instead turning it into a slow, allowing your laner to inflict relatively safe damage as the enemy panics while you burst them down. Landing your Q is crucial for both burst and damage, if you miss it you will do almost no damage to the target, especially early. As for ulting, you have to play her for a bit before you get used to the execute range on it, it's pretty bad early game, but scales very, very well.