If someone has their fingers in your syrup, it's just another way of saying they manipulated you. Cause only slimy people manipulate other people, so their fingers are slimy and sticky because they're covered in your syrup from mucking up your life.
This also has another meaning: chastity. Just imagine if someone wanted you to keep your chastity and they called s.e.x. when someone "puts their fingers in your syrup." That would be pretty effective, right? Cause it's like, super gross.
If you want to manipulate someone else it's going to have a permanent effect on your soul (そう). Being manipulative isn't cool. And your soul will suffer forever for it.