It seems to have variations in heart rate would be the normal response. As blood flow through the heart and brain varies widely during sleep, as do electrical activity in the heart, the elasticity of blood vessels, and the tendency of blood to clot. And all of this activity is just part of a normal night's sleep.
My reference indicates stage 3 is a period of slow heart rate, and stage 4 can can invlove night terrors, etc. and a faster heart rate. The spike would be going from a slow heart rate to the next stage and a faster heart rate and that wouldn't be unexpected.
Thanks for the question, and if you have any further questions or comments you are invited to respond. Take care,
Ken