Heroku does NOT compile files under assets pipelines in Rails 4

Everything goes well in local machine with assets pipeline in Rails 4 and Ruby 2.0. But when deploying to heroku, it is shown that:

-----> Preparing app for Rails asset pipeline
   Running: rake assets:precompile
   I, [2013-03-12T03:28:29.908234 #912]  INFO -- : Writing /tmp/build_1n6yi8lwna3sj/public/assets/rails-2ee5a98f26fbf8c6c461127da73c47eb.png
   I, [2013-03-12T03:28:29.914096 #912]  INFO -- : Writing /tmp/build_1n6yi8lwna3sj/public/assets/trash-3c3c2861eca3747315d712bcfc182902.png
   I, [2013-03-12T03:28:33.963234 #912]  INFO -- : Writing /tmp/build_1n6yi8lwna3sj/public/assets/application-bf2525bd32aa2a7068dbcfaa591b3874.js
   I, [2013-03-12T03:28:40.362850 #912]  INFO -- : Writing /tmp/build_1n6yi8lwna3sj/public/assets/application-13374a65f29a3b4cea6f8da2816ce7ff.css
   Asset precompilation completed (14.36s)

Heroku seems to compile files but put it in /tmp without any errors. My questions are:

1. How come Heroku compile assets files to /tmp?
2. My last solution was to run RAILS_ENV=production bundle exec rake assets:precompile locally, but this generated a manifest-xxxxxx.json in public/assets, rather than manifest.yml, so that heroku doesn't detect the JSON manifest file. I sorted it out by manually created a yml from the json file and heroku became happy. Has heroku's approach been outdated?