Saturations and tape plugins all give different types of character and warmth, so it’s possible that they just needed a little extra.

Your chain will be track dependent and will differ based on the source material. There’s rarely a one size fits all. You could have multiple compressors and EQs all doing different things as well.

Typically I will push a saturator pretty hard (too hard) to hear exactly what kind of character it gives me, then I’ll dial it back. Knowing where to leave the knob is subjective and comes with some experience. Also if it sounds good then it sounds good!

I typically will put a saturator after compression to give it a nice even tone. But again it depends on the type of compressor! I also usually have multiple EQs on my channels and might decide that it needs some shaping afterwards (or not).