If I am the guarantor for someone (say a child, or a younger sibling), and that person got evicted, under what conditions (if any) does this show up on my credit score/report?
You signed papers saying you would be responsible if the renters didn't pay. If the landlord is looking for the money, expect that they will go after you. If you write them a check for what is owed, it will probably not end up anywhere in your credit report.
But if they have to sue you, or put a lien property you own, or garnish your wages, or have a collection agency contact you, expect that it will be noted in your credit report.
If the renters were evicted or they skipped out on the lease, then the document you, the renters, and the landlord signed will discuss damages. It may also discuss procedures. You should review tenant landlord law for the state where the apartment is located. Many states have a small pamphlet that discusses these issues.