In some ways, tucking your chin in may be equivalent to performing a behind the neck press when considering the movement plane of the shoulders and arms. I can tell you from anecdotal experience, that the behind the neck press is contraindicated once you've experienced a rotator cuff tear. And, while a recent study in the Journal of Sport and Health Science found that:
“For participants with normal trunk stability and ideal shoulder ROM,
overhead pressing is a safe exercise (for the shoulder and spine) when
performed either in-front of or behind the head. “
Tucking your chin, in my opinion, does not seem to qualify for “ideal shoulder ROM” and should be considered as improper form as it may result in compromising the ROM to counteract the “tuck”. The simple fact you are asking the question indicates to me that you are aware that there's a potential for improper form on the movements you've indicated. Why take a chance at injury? Work with a spotter, trainer, etc. to ensure that your form is correct.