So, I added my splits.io link to my profile but when I click on it the web address in the search bar becomes:

https://splits.io/users/splits.io%2Fusers%2Fcyiatic

and not

splits.io/users/cyiatic

even though I typed in the latter. Is there anything I'm doing wrong?

My guess is that you put the entire link into the text box, I believe you are supposed to only enter your username, so in your case just "cyiatic" should suffice

Yes, you only put your username in and it will add the https://splits.io/users/ in front of it. Therfore, if you put in just your username it will work.