Without knowing the specifics, we can only guess. However, the red flag in your question is in a matter of days. That is just not possible. For example, search engines are not real-time and will not make rapid changes to a sites search traffic with the exception of trend search and that would only happen if a site already performs well for a particular topic.
SEOs cannot move any needle for a new site if the new site does not have a foundation within the search engine metrics already. This take months. And it is the first few months that are most critical to a site. Low quality scores will doom a site for quite a long time and it will take much much much more work to counter poor SEO work.
How this part of the so-called SEO industry works is trading in bulk work. This is done by reducing labor costs with automation. These sites will bulk submit your site to search engines, directories, and other link friendly based sites. As well, many operate a link authority scheme where a super authority site and several other authority sites intentionally built to manipulate rank and not designed for people. These site will create a link to your site for a price. Anything done by a person is often done by a fairly disreputable person living overseas in India or in Asia. Any link made by a person is barely acceptable if at all and not made with your interest in mind.
Many companies claim white-hat. But white hat in 1995?? 2005?? The fact that they claim white-hat is a huge red flag for me. Why make the claim? Because they operate in a market space where white-hat and black-hat live.
Because of the sheer number of these companies selling bogus claims, directory sites are largely considered junk sites by Google. Link sites too. Smaller search engines cannot return much traffic and are generally useless. The automated links can be easily found by Google as not being natural and will count against your site. The human made links are often predominantly low with a few of moderate quality. The traffic you see is just a splash as a result of the new links and bogus traffic created by the SEO and does not last unless you keep paying them. Keep in mind, that many of these links are often created so that they can be removed.
As far as social media is concerned, it is always temporary. Many of these sites will market your site via social media using boiler plate marketing and automation across a large number of social media sites. This gives a short blast of traffic but does not last.
As far as advertising is concerned, if any of these sites do any advertising, it would be on lower quality sites with lower quality ads.
The name of the game is to not only sell you something, but keep selling you something. Many of these sites trade on ignorance and expect that you will not know quality traffic from junk traffic. They can easily drop your traffic quickly if you chose not to renew and will. Any link they create will be mostly low quality with some more moderate quality links. While this sounds good, in the end it will not really benefit your site. For many of these sites, the name of the game is to automate as much as possible, use low value human capital in poor parts of the world to do any manual work, and to keep you on the hook.
Again, there is no such thing as rapid results in the SEO world. Anyone who promises results is lying. No SEO can really promise results, only improvements that result in traffic later. Certainly, no SEO can promise rapid results without artificial traffic and techniques that are technically white-hat and still considered spam even if it is on the edge.