iPad backup and restore: OK, but where are my apps?

I'm currently traveling with my second computer, a MacBook Air. My main iMac back at home is what I use for my iTunes library and iPad syncing. I just got a new iPad and want to sync all my apps and info from my previous one. So I connected it to my MBA and backed it up to iCloud using iTunes. Then I connected the new iPad and chose to restore from the latest backed up version. All went well, except that none of my 3rd party apps appear on the new iPad. Shouldn't these have been included in the backup? It will be another month before I'm back home where my main Mac is with all my apps on it. Does that mean I have to wait until then to restore all my many many dozens of apps and their data? I can't possibly handle the idea of having to manually reinstall all these apps from the App Store in the meantime, and anyway the data I have stored in them won't be reinstalled.

I'm a longtime Mac user but I can't figure this one out. Thanks in advance for your help.