It can be done using Adobe After Effects and the Bodymovin plugin.

I’ve used BounceJS in the past: http://bouncejs.com

Most tools put out a lot of unnecessary code and often rely on JavaScript, so my guess would be that this is handwritten. The animation consists of three phases for each element, which they reordered using pixel value transforms. The background containers are fixed in place and the opacity is changed depending on stage 1/2/3. To ensure them not having to adjust any values for smaller devices, they scaled the parent element to fit the browser size. Time consuming, but the best way to get the performance you need.

http://animista.net/ is quite handy for quickly putting something together.