Ari is completely based on your sanity meter. Her checking on you is random, however regardless of your meter. If it's below 1/4th while she is checking on you, this causes her to attack based on my experience. Use the plushie on the desk to regain sanity, however keep in mind that rapidly spamming the plush will cause Misty to get angry and attack.
Your best option when using the plush to keep Misty from freaking out is to give it about 3 squeezes, then pause for a few seconds and repeat. Don't panic and just spam the plush.
I believe the plush works the same way as the original did in the Unreal Engine build, only the Heat gauge is not visible. In the original build, every time you squeezed the plush, the heat gauge would rise and if it filled, it the plush would pop. In this version, when the Heat gauge is maxed, Misty triggers. From my experience, this gauge is exponential based on time. Meaning that three slow squeezes is more effective than three fast squeezes, because it actually causes the heat gauge to increase at a slower rate, while still giving similar results. Likewise in this version, squeezing the plush rapidly is more likely to trigger a Misty attack than using slow, steady squeezes to maintain your bar. Keep your squeezes to roughly 3 or 4 at a time, then take a second before doing it again. Doing this should more or less keep Misty from attacking at all, unless her door happens to be open.