Hellbound: Hellraiser II Clip - Desire | 4K 

They didn't have humanity. They had sensibility. They didn't spare Tiffany because she was innocent, but because she genuinely had no desire to explore the puzzle.

He was there to turn up the volume in Hellraiser III

They have rules, not humanity. They're lawful evil, unlike most slasher monsters.

Until Hellraiser III, the Cenobites used to be human, including Pinhead (he was Captain Elliot Spencer). Before Dr. Channard (as a Cenobite) bloodily kills them, Kirsty Cotten reminds them that they were once human, therefor having humanity. The pinhead in Hellraiser III consisted of the plain leftovers of the excess "Evil" that Elliot had grown, and that is another story. So yes, I believe Pinhead in Hellraiser II was part Elliot Spencer, and before he was exposed as "once human" had at least some empathy. -Including the decision not to kill the girl. Pinhead in hellraiser III wouldn't of only killed her, but enjoyed it at the same time.

The third and later movies are so far removed from the story these creatures were based on it is a travesty.

Well technically she did have visitors.

I suppose u could argue that kirsty technically did have desire in calling them down to her morbid curiosity of what the box is, what it does and why frank was so protective over it

Kristy unknowingly did what she did...... Hands and curious hands called them in the first movie. What Pinhead meant by desire called them meaning Dr. Channards desire of wanting the box opened called them.

Because Kirsty had desire. Desire to solve the puzzle box and understand what Frank and Julia were up to. But also desire for her own pleasure (the film does portray her as someone about to get sexual with her boyfriend Steve). Kirsty didn't know about the Cenobites, but she had everything "in her" to be a perfect recipient for their twisted dogma. Tiffany, on the other hand, was pure and innocent.

Pinnnhead

The line makes sense though. Pinhead is saying Tiffany physically solving the puzzle isn't what called them, it was someone else's desire, Channard's. But they mistakenly believed it was Kirsty.

They would've taken her despite her innocence. So long as she was CURIOUS, she would've been subject to their torment but since she was misled and didn't understand the box, they set her aside and sought the one who DESIRED the box.