Re: ....and good question..
I get the impression from the website that (to them at least) a soul tie is more than just an association (you might say "yoke"), yet they stop short of saying something like "possession".
But the verses they cited don't really seem to support what they're saying. The familiar Biblical phrase "one in spirit" means of one purpose, having the same "mind", being united in a belief. We believers all have the same Holy Spirit, but our spirits are united with Him, not each other. Yes, we can feel close to people, but I draw the line between "close" and "knit".
Soul ties seems to mean that somehow the souls are spiritually joined in the sense that they are "attached" or "blended". While no one would argue with the need to renounce past sins, I have the impression that the supporters of the soul ties concept believe that this is not enough, that somehow certain special things must be done to untie the souls. This is what I disagree with.