the animals can actually change form and it's not just an illusion?
I don't believe there is a real answer, just some theories.
spoiler alert
To answer the question you have to look at the previous Petshop of Horrors Manga, the petshop of horrors that was published between 1995 and 1998.
I'll answer referring to this manga.
When reading the old petshop of horrors you'll believe seeing those animals has to do with the incense Count D is burning. However, in this theory there are a few inconsistencies.
These inconcistencies have to do with the other main character Leon Orcot (a character TaiZuu has to replace) and his little brother: Chris Orcot.
Count D takes care of Leons brother Chirs. Chris is mutistic (he doesn't speak). Chris's mutism goes together with the fact that he 'rejected' the outside world. Therefore Chris can see all the animals like Pon-chan and Tetsu in human form. The four of them speak trough thought.
Leon Orcot - the great sceptic - never saw the human form of any animal, and even the animal that shapeshifts after whatever someone likes to see: Leon sees it's true form. Along the series Leon learns to communicate with those animals trough thought as well.
The only time the incense seems to really have effect on Leon is when he follows Count D to a natural historic museum where Leon sees real prehistoric animals in some sort of sleep.
At the very end of the series when Chris embraces the outside world and steps over his mutism, he loses his ability to speak with the animals, or to see their true form in instant.
At the very end of the manga we find out the incense and tea from the count were investigated by the police: totally clean: no toxins whatsoever.
It's almost as if Matsuri-sensei wants to suggest it all has to do with the power of imagination, and the openmindedness to accept a 'true' form.
So what makes this of D?
In the end Matsuri-sensei explains D is from a different race than the human race. D isn't a vampire. D's race orginates from China, his ancestors lived in a remote area of anicent china that is now known as the kunlun mountains. His race was able to understand the speech of animals and began to know them as friends. They would convey to the local villagers the prophecies told to them by the sacred beasts. D's race was however slaughtered, one survived, and his hatred reïncarnated. Or something like that.