I see a lot of interaction designers are using tools like quartz composer, origami, adobe after effects to design interactions. What benefits does it bring to web app and native app design?
This is often people who want to show animations etc that don't know how to code and/or haven't come across any interactive prototyping tools. The benefits are that they can pitch things to stakeholders etc easier and also it can be a useful tool for communicating with devs what you are hoping to achieve interaction-wise. That said, it also leads to designers having unrealistic expectations about what can be achieved because they've made it do something funky in a video.
The clients always wanted to know how the app or a web page look like and even they have their own designs in mind. To fulfill their requirements the Interaction designers design prototypes that looks and feels exactly how the app will come out as a finished product. This can be achieved using tools like quartz composer, origami and adobe after effects etc.. as you mentioned. This gives customer satisfaction and it can also be used as a reference by programmers while developing the product.
Also, now that the gap between motion design and usable code is slimming, it is even more useful to create delightful experiences for users. The aesthetic aspect of a product helps mask some compromises made in UI.