There can be many reasons for muscle spasms/pulls in the neck area, including (in no particular order):
- Insufficient food: the muscles lack the glycogen stores required and overcompensate
- Insufficient sleep: your nervous system is impacted when you are in a sleep deprived state, and I've had most of the neck spasm issues when in this state
- Bad hydration: electrolyte imbalances can cause spurious pain signals or muscle spasms to occur.
- Upper back weakness: the upper back and rear delts aren't doing their part to contribute to the lift and so you are straining to do the lift
- Bad form: your spotters may not know what to look for or aren't really paying attention more than to keep the bar from crushing your neck
You may even have a combination of multiple factors going on at the same time. Don't rule out "Bad Form" unless you have a qualified coach tell you that your form is good. Someone who is spotting is just looking out for safety, not how to get more muscle into the bar.
I'm going to assume that the food, sleep, and hydration are all working good enough for the remainder of the answer, but please make sure they are not the issue.
Pressing Things Overhead
The different variations of pressing things overhead require your upper back to be engaged and transition the weight from in front of your head to directly over your shoulders. In fact, you should be able to draw a straight line from the center of the barbell, through your shoulder blades, and your mid foot. Your lower back should also be in a neutral position.
If you are not ending in this position, chances are the bar is remaining in front of you. Chances are also good that your upper back is not involved in the lift at all.
Bench Pressing Things
Refine your technique, but don't change it completely. There is a time and place for flat back with feet on the bench, but it is to isolate the arms if they are the weakness.
Arching your back is a good thing, but do make sure of the following things:
- Your shoulders, butt and head need to be in contact with the bench (notice I did not say neck).
- The bar will vary where it hits when in the bottom position, but it should be between the nipple line and the sternum.
- The bar path should end with the bar directly over the shoulders and the shoulders remaining in contact with the bench (do not raise the shoulders). That means the bar will move a bit horizontally. It also means your upper back is involved to assist.
Take a little weight off the bar, and focus on the start and end positions. Also try to activate your upper back to help on these lifts.
- Start with a weight you can perform the movement slowly, and focus on staying in the strongest body position at all stages of the lift.
- Your progression will be to add more speed to the bar before adding weight. Each time you increase weight start over with a slow lift
- Perform dumbbell front raises as an assistance exercise. Start with a weight you can do 3x10 with.