Something similar happened to my saddle but with rain splashes when it was tipping it down and I was faffing about getting tacked up. I was very disappointed at the way it marked the saddle/ cantle area.. My saddler suggested neatsfoot oil or a really good leather oil and it worked a treat after a few applications. I now have no marks on my saddle.
Oiling thicker leathers is okayish, oiling the fine leathers on seat, knee pads and panel is not advised, you'll end up with a stretched out seat which will look like the tree might be broken!
Use waterproof saddle covers in heavy rain, all leather will mark to an extent, lighter brown leathers may show it more.
I use my waterproof riding skirt if it's raining, which covers the whole saddle. Unfortunately, the woman who used to hack her occasionally didn't use anything.