Keep in mind that those spammy websites will not last longer in the 1st place, this is called churn and burn.
There are different methods to achieve this, as others have said noone will reveal the exact technique they are using but there is a lot of variations black hatters use like: Private PBN (Most common), Trusted Sape links, High DA redirect, etc.
If you can share some of those keywords i can try to do reverse engineering to determine witch method they are using, but there is also techniques to hide your method so is not 100% that we will discover everything they are doing to rank.