This sounds like malware. Maybe try clearing your browsing data (make sure to create a backup of your Twine projects) and running a scan, if possible. It's odd that its happening to you on two systems, but not completely unheard of; wherever the infection came from, it might be a source you visit on both.
Testing on my own iPad, I'm not having this issue, but that's really neither here nor there. Twine is completely ad-free, open source, and non-commercial as far as I know.