This was possible for a number of reasons. Firstly, TV pictures require less memory and less computer power to manipulate than film. Thus animation and modelling times were fast but costs kept low. This is because whilst computer graphics are good, they're better for long distance shots. Animatronics are more realistic in close up work, such as when a dinosaur is eating or drinking.
Construction is a painstaking process.
Initial models are made in clay, then a series of inverse moulds are made from which the final product is produced. Mounts are added for handholds plus motors to operate the nostrils, eyes or other body parts. Walking with Dinosaurs is ground-breaking in many ways. Pulling all the research into a cohesive set of programmes is a momentous task in itself. Making it interesting, entertaining and informative is yet another.