600 series Medtronic pumps and OmniPods are IPX8 rated. Both should be safe to go into a hot tub for short periods of time, provided they are not damaged. Any damage, like cracks or loose seals could allow water into your pump.
Tandem pumps are IPX7 rated. By that definition, Tandem pumps should be able to be submersed, but Tandem does not recommend it. (Summer-Friendly Tandem Pump Features, tandemdiabetes.com)
If you are still concerned about submerging your cortisol pump in the water of a hot tub, you can always place it on the edge outside of the water. Depending on where your infusion site is, the tubing could be long enough to allow for the pump to remain out of the water.
However, be careful with your inset. Soaking in hot water will weaken the adhesive. This can be mitigated through the use of additional adhesive patches, such as GrifGrip (this link will get you 10% off your first order). It is wise to limit hot tub time to 10-30 minutes. Even so, your inset could become compromised. Do not go into a hot tub if you do not have back-up insets for your cortisol pump.
Frequently Asked Questions. (n.d.). Retrieved from https://www.myomnipod.com/podder-support/faq.
Longman, J. (2019, August 29). IPX Ratings Explained. Retrieved from https://www.audioreputation.com/ipx-ratings-explained/.
MiniMed™ 630G Insulin Pump System. (n.d.). Retrieved from https://www.medtronicdiabetes.com/products/minimed-630g-insulin-pump-system.
Summer-Friendly Tandem Pump Features. (n.d.). Retrieved from https://www.tandemdiabetes.com/blog/post/general/2017/07/13/summer-friendly-tandem-pump-features.