Psuedo-Imaginary Dinosaurs are the servants of Tyroganon Ferox, the Paradox Lord of the Infinite Boneyard. No other creature would (or could) serve the lord of temporal paradoxes.
These creatures are halfway real. When a psuedo-imaginary dinosaur appears, everyone who sees it is is allowed to disbelieve it. Characters who suceed realize that the dinosaur has no mass or energy and cannot harm them, and the dinosaur becomes nonexistent (as far as they are concerned), and vanishes from their mind and memory. Characters who fail their save realize that the dinosaur is thinking, hateful creature, and the dinosaur is real (as far as they are concerned).
Combat only gets interesting if some people make their save while others fail it. Players who have ignored the dinosaur cannot affect it or interact with it in any way, and vice versa. On the other hand, players who failed their save may be crushed, knocked about, or even picked up and swallowed by. To their more willful companions, they appear to be flying through the air and leaking blood for no reason.
Technically, the dinosaur is reflecting itself off the mind of its victim. The people who failed their saves have a small part of their minds hijacked, and it is this part of their mind that is actually performing telekinesis in imitation of a dinosaur that isn't real (in the strictest sense of the word). Psuedo-Imaginary Dinosaurs are not dinosaurs at all, but malevolent dinosaur consciousnesses brought through time by the Lord of Paradoxes. They are not astral bodies or ethereal monsters. They are minds looking for a brain.
Bottom-line: if you kill or knock unconscious the people who are imagining the dinosaur eating them, the dinosaur will dissipate. The dinosaur will try to prevent this, of course.
The halflings of the psychogenic jungles know this. A fortress with no one in it will never be molested by imaginary dinosaurs, but if one halfling passes through, catches sight of one of Tyroganon's servants and believes in it, the entire fortress can be destroyed by the psychic echoes of this thing from their own brain.
Consequently, many of the halflings are experienced in the use of the lead button, which is a heavy (usually-lead) button sewn on the inside wrist of their jackets. Halflings who see and believe in dinosaurs know to quickly knock themselves unconscious with it before the dinosaur can tear them apart.
The dinosaurs come in all shapes and colors that you can imagine, literally. And sure--they sometimes incorporate elements of what you are thinking about, your greatest fears, whatever. They are intelligent enough to follow a 'believer' back to a larger group where they can get more people to believe in them.
DM's Notes: Don't overuse these guys. Sometimes combat will occur where four PCs will be fighting a dinosaur while the fifth PC just watches them, completely unable to help. PCs can choose to fail their saving throw, but this must be done at the same time as everyone else.