I will start off the discussion on Ayla vs. Raelynn, but feel free to contribute, especially through the discussion section, but if you feel you are an experience Ayla or Raelynn player, don't hesitate to add wisdom, and maybe alter the score.
Raelynn is a relatively slow naut, with a low jump. The slow portion of Evil Eye will reduce raelynn's jump height, making it difficult for her to escape. Raelynn has no double jump, so landing the eye can be as simple as waiting for her to drop out of her fall, or stop to snipe.
Low health evil eyes are not advised unless you have just seen Raelynn use her snipe, and know it's safe to advance, or are escaping another battle and come across Raelynn.
Once you can survive a snipe easily, after buying health upgrades, you may be able to initiate on Raelynn if her team is not there to back her up. In this situation, it is quite possible to finish her off with an Evil Eye, or you may wish to initiate with Evil Eye to add the slow, making it easier to hold Rage.
Due to her boots powerup, Raelynn may be able to avoid Rage, however her low jump means she is a much easier target than many opponents. As always, focus on using rage to take out creep waves, to save your allies' burst abilities, but beware of being sniped.
If Raelynn stops to snipe while out in the open without her team (overextended), it may be possible to use this to your advantage by engaging on her using Rage. It is especially hard for Raelynn to target you if you move around and across her at high speed. If you avoid the snipe, then great. If it leaves you on low health, it might be time to fire off a quick eye to prevent her following (or kill her) and make a quick getaway.
Beware Timerifts, and be prepared for Raelynn to drop one down between you.
Not Ayla's most well used tool. The extra health will help you to shrug off Snipe, Sometimes Chain Whack can be used to secure a kill if you miscalculated your Evil Eye damage. If Rage is on cooldown, you may need to use Chain Whack on droids. Not much to say here really.
As snipe can go up to 75 damage, it is important to stay back while Raelynn is using it, or be prepared to go to base a lot. It is most worrying to Ayla early game. By midgame (lvl 15-20), Ayla can use Raelynn's stillness to her advantage to go in for the kill, as health upgrades make her less worried about the damage.
Timerift is Raelynn's main tool to use against Ayla. She may place them at choke points to prevent you following (e.g. places where turrets used to be, or adjacent to the central drop-through platform on Sorona). If Raelynn places a time rift after you start Rage, it may be best to turn back. Bide your time. Wait for Raelynn to waste her timerift, or engage far from choke points (or while she is sniping!)
Raelynn's gun can be kind of hard for ayla to dodge, and if she is speccing into gun with HC-bomb, she may wish to use preloaded shots, time rift, more shots, and combo with snipe for the finisher. In general Raelynn's gun does a lot of damage, but most Raelynns spec into Snipe first. Try to maintain side to side and up and down motions to juke gun shots, and be ready to hide behind scenery if she gets you low enough to snipe.
Overall, Ayla has a favourable matchup against Raelynn, as Raelynn's only crowd control (Timerift) is static and avoidable, and Raelynn herself is often static, leaving her highly susceptible to Rage (and fights may turn around when Rae tries to snipe you - if you think you can kill her before she fires it, go for it).
I rate this matchup as an 8 in favour of Ayla. Raelynn can counter some of Ayla's plays, however she has a low jump, and is highly susceptible to Rage.