Further, obviously the seed video that you used is going to have an enormous influence on subsequent videos (as presumably would the sender -- shared links can contain details about the sender, and if they had a logical algorithm that can play a part as well). And of course surely we all know that sites don't just track by being logged in. Even if you clear all cookies.
I just opened the TikTok homepage through a proxy in a clean instance of Firefox. First video was a woman who paints patterns on her face. Second was someone show a technique to clean stainless steel sinks. Third was a guy in Turkey showing his rugs. Then a dog bringing a leash back to its owner, someone using one of those pop-it distraction things, a guy with his cat in a box in front of a roller coaster video pretending the cat is on the roller coaster.
Eh. I don't see how your anecdote is such strong evidence of the "type of audience they were aiming to attract" (especially when the site seems to overwhelmingly cater to adult women...)
I click a link in WhatsApp, it opens up Safari in iOS on my phone, it plays the video, then at the end it starts playing another video.
I'm using a content blocker, so I presume TikTok does not know anything about my personal characteristics, so I assumed the videos that autoplay are the ones they autoplay by default.
PS I will forever harbor resentment to people around the world for putting up with video players that lack the ability to skip around the video or even see the length of the video.
If someone sent you a link, it will include an identifier of the sender. It usually will say at the top of the screen "[Sender account] is using TikTok! Join now". Logically this informs the suggestions of the app.
The lack of scrubbing is annoying (although apparently the Android version recently added the ability). The app is also inconsistent in that sometimes it shows a progress indicator at the bottom, sometimes it doesn't.