They change the page client-side, which introduces a problem they call “flicker”. It just means that for a moment you see the server-side rendered page as-is, then the tool hacks it into something else, depending on which group you’re in. This can obviously be jarring. The “flicker” is overcome by a page-hiding snippet that shows the page after the tool has done its dirty business or after a timeout (typically 3s).
Often, these tools aren’t used for multivariate testing at all. They’re used because the marketing team doesn’t want to go through the web team, so they get an exec to force the web team to install the tool (along with 50 other pieces of marketing crapware) so marketing can hack its changes into the website after it’s loaded. It’s not uncommon for these tools to completely break the website, because the web team makes a change that breaks assumptions relied upon by the marketing team’s hacks.
Often, the marketing team will have these changes made by a developer who they hire directly. They are unqualified to interview developers and this is one of many ways incompetent developers find employment.
The ability to use an injection tool and hire devs for small changes on quick turnarounds can be massive in enabling the marketing department to move forwards.
And yet another side shows sites deliberately engineered this way to allow agile behaviour by non-devs. I've seen a few where they track an internal metric so that a dev somes and consolidates it all before it gets too bad.
Also, it’s terrible for SEO.