There are two things on the tuba that make it hard to play fast runs -- the valves and the pitch. The valves are big and have a lot of travel, and they have fairly strong springs. Moving them fast and accurately requires training your muscles as well as your brains. This requires practice.
The low pitch of a tuba means there's a bigger time lag between when you decide to play the note and when you hear it than in most instruments. It also means that you can achieve a lot of pitch variability with your lips, which needs to be controlled. This also requires practice.
Practice a lot of scales, chromatic and otherwise, tonguing each note. Start slow so you can get each note on time and on pitch, and increase your speed as fast as you can play it close to perfectly.
After you have that down, play the same scales slurring the notes. This will be pretty easy until you get to the low notes.
When you can play scales fast, tonguing and slurring, then start with some arpeggios. Some technique books will have some good ones, or you can just play arpeggios of chords in different keys. Learn to do this with two notes tongued and two notes slurred, or all of them slurred -- it will help your control a lot.
One other thing that's important is to bend your fingers. You can move the valves a lot faster and more accurately that way.