Hi Josh
If I am reading this correctly it does sound like the tibialis posterior or possibly flexor digitorum or FHL. As with most tendon injuries, anything more than a couple of days rest is rarely helpful, as tendons respond best to loading.
Some of my go to exercises are linked below. Isometrics (standing on tip toes) can be helpful at first to decrease pain. Quickly move on to more active loading exercises as pain improves. I like 2 legged calf raises with a ball squeeze (see below):
I also like heel raises on a slant board – so that the foot is everted (example in the video below).
Simple band work to add resistance to ankle inversion is beneficial, as well as intrinsic foot muscle strengthening exercises – look up ‘foot core exercises’.
Lastly, this is an injury where a simple arch support can give good relief for day to day weight bearing activities, and during hikes/runs.
The risk of rupture is low, and typically is only seen in the extremely obese, or if there is a major tear in the tendon (not likely unless a big slip/fall/twist).
Flatter hikes will be better tolerated at first, so avoid steep hiking until you see improvement.
Do the exercises every second day and add more load as they start to feel easier.
Hope that helps. Fire me an email at andy@evokeendurance if additional advice is needed.