Culpeper assigns saffron to the Sun, on the colour and on the cordial action attributed to it. The reasoning is colour-based and therefore signature reasoning, but reinforced by something else: saffron's cost made it a status substance, and status attaches to the most dignified planet. A dye reserved for the robes of kings and priests was never going to be filed under Saturn.
Culpeper's entry contains a detail worth quoting for its strangeness. He holds that a moderate dose gladdens the heart and quickens the senses, but that excess is dangerous and provokes immoderate laughter, death by laughing is a claim that appears in several early modern sources on saffron. It is not a pharmacological description of anything saffron does. High doses of saffron are genuinely toxic, with an estimated lethal dose in the region of several grams, but the syndrome is bleeding and organ damage, not hilarity.
The plant's documented history reaches much further back than the herbals. Saffron crocuses and saffron-gatherers appear in the Bronze Age frescoes at Akrotiri on Thera, dating to before the mid-second millennium BC, in scenes that appear to show harvest and possibly a ritual or medical context. That is direct archaeological evidence of saffron culture roughly three and a half thousand years old, which is a far stronger foundation than anything the correspondence literature supplies.
Modern research interest has focused on saffron extracts and depressive symptoms, where several small trials have reported positive results and the evidence base remains limited and preliminary.