Yes, formally. You don't have to specify -z in GNU tar today, you can just say -x and it'll add -z or -j for you -- it figures out on the fly if the archive's been compressed and how. Very convenient.
instead of make install, consider checkinstall or fpm so that you are properly integrated into ubuntu's native package manager (dpkg). Doing so will save you headaches when you want to uninstall tmux or upgrade later.
Well the easiest way is either to wait for it to appear in the repos or wait for someone to package it and put it into a PPA. However, it doesn't have that many dependencies, so building it yourself is another not too stressful option.
I continue to be amazed by the people who install "random binaries" via PPA.
I guess I assume that if you want cutting-edge packages you'll use a cutting-edge release/distribution. If you don't, and you want something more recent then it seems to make sense to make your own packages, or install locally via gnu-stow, or similar.