The way how it worked is that the spammer used my urllengthener as a redirection service to a website that looks like an incomplete project, which is actually a disguise. There's javascript code on their site that if there's a URL fragment identifier (the hash thingie postfix for URL) detection mechanism and if the URL fragment identifier matches an ad of their own, it'd redirect to the actual spam ad.
Let's say the spammer owns example.org. The spammer would generate link with my service such that https://urllengthener.sadale.net/foobarbaz would redirect to https://example.org. Then it'd send spam with a link of https://urllengthener.sadale.net/foobarbaz#identifierXYZ to the victim. Then the victim would click on the link, which redirects him to https://example.org/#identifierXYZ, which would show victim the ad. https://example.org/ looks legit on its own and there is no log shown on the HTTP server because the URL fragment identifier is a client-side thing. I'm kind of thankful of that spam abuse report. Otherwise I might have never found out.
(Remarks: example.org isn't the actual spam site. I just use this domain name as an example.)
I don't have the time for now but I think I should make a write up about that some time later.
And I've tested your service and apparently your site is vulnerable for the exact same kind of abuse as mine. I'd strongly recommend you to at least disabling redirection of URL fragment identifier. Example of URL that's prone to abuse: https://looooooooooooooooooooooooooooooooooooooooooooooooooo...