Yes, what you are seeing with your HR is normal. Recovery after hard exercise involves many different hormones, which do different things at different speeds.

The best way to take morning resting HR is to get up, use the bathroom, get dressed, and start your morning routine. After a few minutes, put on the transmitter, and lie down. Your HR will settle on a number after a few minutes. You can also take your morning standing HR after taking your resting HR: stand up and record your HR after 2 minutes of standing. These are separate numbers, not to be averaged. An increase of 5-8 beats in your morning resting HR indicates lack of recovery from training, illness, or partying - don't exercise hard until it goes back down. An increase of 10 beats in standing HR indicates a prolonged period of hard training. Again, back off the intensity until it goes back down.