Are you using very hot water? Too warm?

Another thought is that your circulation in the feet is poor, and they are cold. When warming up, they may feel tingly or burn.
This is like when you go out in the snow and get really cold, and then warm up... hands and ears may tingle?

There are two sets of sensory temperature nerves in the hands and feet. Heat sensing ones and cold ones. The cold ones take over precedent sensations because of their survival value. So when they are active, the heat ones don't get thru to the spinal cord to register heat. This is why certain rubs with high menthol content work well for burning sensations in the feet. Biofreeze is one example. Menthol stimulates the cold sensing neurons.

You can try putting something like Biofreeze on them after the soaks. Or you can take oral magnesium instead.
People vary in the sensations they get in their feet with PN. I get burning mostly. But others get stabbing pain instead.

Check the temperature of the soaks you are using. I would try to get used to the soaks. Say everyday for a week. Your reaction may dissipate as the magnesium starts working.
If not, nothing is lost, you will then have to try Biofreeze.

If your PN is highly compressive, say because of ligament pressure on the foot, you may have to experiment further with topical products. Lidoderm patches may help.

I'd like to add: If you put too much epsom salts into the water, it may irritate the skin...just like salt would.